diff --git a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp
index 28c8bea6915..1892df87e98 100644
--- a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp
+++ b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp
@@ -6,7 +6,6 @@
 #include <CGAL/Delaunay_triangulation_2.h>
 
 #include <CGAL/algorithm.h>
-#include <CGAL/assertions.h>
 
 #include <fstream>
 #include <iostream>
diff --git a/BGL/examples/BGL_surface_mesh/surface_mesh_partition.cpp b/BGL/examples/BGL_surface_mesh/surface_mesh_partition.cpp
index 50ec6b0affa..57c96a907d8 100644
--- a/BGL/examples/BGL_surface_mesh/surface_mesh_partition.cpp
+++ b/BGL/examples/BGL_surface_mesh/surface_mesh_partition.cpp
@@ -7,6 +7,7 @@
 
 #include <fstream>
 #include <iostream>
+#include <cassert>
 
 typedef CGAL::Simple_cartesian<double>                           K;
 typedef CGAL::Surface_mesh<K::Point_3>                           SM;
@@ -39,7 +40,7 @@ int main(int argc, char** argv)
   // Extract the part n°0 of the partition into a new, independent mesh
   typedef CGAL::Face_filtered_graph<SM>                            Filtered_graph;
   Filtered_graph filtered_sm(sm, 0 /*id of th part*/, face_pid_map);
-    CGAL_assertion(filtered_sm.is_selection_valid());
+  assert(filtered_sm.is_selection_valid());
   SM part_sm;
   CGAL::copy_face_graph(filtered_sm, part_sm);
 
diff --git a/Generator/examples/Generator/random_segments2.cpp b/Generator/examples/Generator/random_segments2.cpp
index d13c64c333b..f8c4fa99f62 100644
--- a/Generator/examples/Generator/random_segments2.cpp
+++ b/Generator/examples/Generator/random_segments2.cpp
@@ -8,6 +8,7 @@
 #include <CGAL/function_objects.h>
 #include <CGAL/Join_input_iterator.h>
 #include <CGAL/Counting_iterator.h>
+#include <cassert>
 
 using namespace CGAL;
 
@@ -41,16 +42,16 @@ int main() {
     Count_iterator t2_end( t2, 50);
     std::copy( t2_begin, t2_end, std::back_inserter(segs));
 
-    CGAL_assertion( segs.size() == 100);
+    assert( segs.size() == 100);
     for ( Vector::iterator i = segs.begin(); i != segs.end(); i++){
-        CGAL_assertion( i->source().x() <=  250);
-        CGAL_assertion( i->source().x() >= -250);
-        CGAL_assertion( i->source().y() <=  250);
-        CGAL_assertion( i->source().y() >= -250);
-        CGAL_assertion( i->target().x() <=  250);
-        CGAL_assertion( i->target().x() >= -250);
-        CGAL_assertion( i->target().y() <=  250);
-        CGAL_assertion( i->target().y() >= -250);
+        assert( i->source().x() <=  250);
+        assert( i->source().x() >= -250);
+        assert( i->source().y() <=  250);
+        assert( i->source().y() >= -250);
+        assert( i->target().x() <=  250);
+        assert( i->target().x() >= -250);
+        assert( i->target().y() <=  250);
+        assert( i->target().y() >= -250);
     }
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_color.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_color.cpp
index adcfdc0c5fe..ce64abdac99 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_color.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_color.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/HalfedgeDS_items_2.h>
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/IO/Color.h>
+#include <cassert>
 
 // A face type with a color member variable.
 template <class Refs>
@@ -30,6 +31,6 @@ int main() {
     HDS hds;
     Face_handle f = hds.faces_push_back( Face( CGAL::IO::red()));
     f->color = CGAL::IO::blue();
-    CGAL_assertion( f->color == CGAL::IO::blue());
+    assert( f->color == CGAL::IO::blue());
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact.cpp
index 2c6844a496b..04690850cce 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact.cpp
@@ -2,6 +2,7 @@
 #include <CGAL/HalfedgeDS_vector.h>
 #include <CGAL/HalfedgeDS_decorator.h>
 #include <cstddef>
+#include <cassert>
 
 // Define a new halfedge class. We assume that the Halfedge_handle can
 // be created from a pointer (e.g. the HalfedgeDS is based here on the
@@ -55,15 +56,15 @@ public:
                                     (nxt & (~ std::ptrdiff_t(1))));
     }
     void  set_opposite( Halfedge_handle h) {
-        CGAL_precondition(( &* h - 1 == &* HDS::halfedge_handle(this)) ||
-                          ( &* h + 1 == &* HDS::halfedge_handle(this)));
+        assert(( &* h - 1 == &* HDS::halfedge_handle(this)) ||
+	       ( &* h + 1 == &* HDS::halfedge_handle(this)));
         if ( &* h - 1 == &* HDS::halfedge_handle(this))
             nxt |= 1;
         else
             nxt &= (~ std::ptrdiff_t(1));
     }
     void  set_next( Halfedge_handle h) {
-        CGAL_precondition( ((std::ptrdiff_t)(&*h) & 1) == 0);
+      assert( ((std::ptrdiff_t)(&*h) & 1) == 0);
         nxt = ((std::ptrdiff_t)(&*h)) | (nxt & 1);
     }
 private:    // Support for the Vertex_handle.
@@ -99,6 +100,6 @@ int main() {
     HDS hds(1,2,2);
     Decorator decorator(hds);
     decorator.create_loop();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact2.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact2.cpp
index ff101610451..6c8ff61f26f 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact2.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_compact2.cpp
@@ -2,6 +2,7 @@
 #include <CGAL/HalfedgeDS_list.h>
 #include <CGAL/HalfedgeDS_decorator.h>
 #include <cstddef>
+#include <cassert>
 
 // Define a new halfedge class. We assume that the Halfedge_handle can
 // be created from a pointer (e.g. the HalfedgeDS is based here on the
@@ -54,15 +55,15 @@ public:
                                                  (~ std::ptrdiff_t(1))));
     }
     void  set_opposite( Halfedge_handle h) {
-        CGAL_precondition(( &* h - 1 == &* HDS::halfedge_handle(this)) ||
-                          ( &* h + 1 == &* HDS::halfedge_handle(this)));
+        asseert(( &* h - 1 == &* HDS::halfedge_handle(this)) ||
+		( &* h + 1 == &* HDS::halfedge_handle(this)));
         if ( &* h - 1 == &* HDS::halfedge_handle(this))
             nxt |= 1;
         else
             nxt &= (~ std::ptrdiff_t(1));
     }
     void  set_next( Halfedge_handle h) {
-        CGAL_precondition( ((std::ptrdiff_t)(&*h) & 1) == 0);
+        assert( ((std::ptrdiff_t)(&*h) & 1) == 0);
         nxt = ((std::ptrdiff_t)(&*h)) | (nxt & 1);
     }
 private:    // Support for the Vertex_handle.
@@ -98,6 +99,6 @@ int main() {
     HDS hds;
     Decorator decorator(hds);
     decorator.create_loop();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_default.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_default.cpp
index 766d8d287ce..3f570bfa960 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_default.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_default.cpp
@@ -1,5 +1,6 @@
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/HalfedgeDS_decorator.h>
+#include <cassert>
 
 struct Traits { typedef int Point_2; };
 typedef CGAL::HalfedgeDS_default<Traits> HDS;
@@ -9,6 +10,6 @@ int main() {
     HDS hds;
     Decorator decorator(hds);
     decorator.create_loop();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_edge_iterator.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_edge_iterator.cpp
index 494552136f6..4e0d8fb6a42 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_edge_iterator.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_edge_iterator.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/HalfedgeDS_decorator.h>
 #include <CGAL/N_step_adaptor.h>
+#include <cassert>
 
 struct Traits { typedef int Point_2; };
 typedef CGAL::HalfedgeDS_default<Traits>            HDS;
@@ -13,10 +14,10 @@ int main() {
     Decorator decorator(hds);
     decorator.create_loop();
     decorator.create_segment();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     int n = 0;
     for ( Iterator e = hds.halfedges_begin(); e != hds.halfedges_end(); ++e)
         ++n;
-    CGAL_assertion( n == 2);  // == 2 edges
+    assert( n == 2);  // == 2 edges
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph.cpp
index 32c087268ea..f5e7a26a443 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/HalfedgeDS_min_items.h>
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/HalfedgeDS_decorator.h>
+#include <cassert>
 
 // no traits needed, argument can be arbitrary dummy.
 typedef CGAL::HalfedgeDS_default<int, CGAL::HalfedgeDS_min_items> HDS;
@@ -10,6 +11,6 @@ int main() {
     HDS hds;
     Decorator decorator(hds);
     decorator.create_loop();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph2.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph2.cpp
index e33ec754b24..e042370de9a 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph2.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_graph2.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/HalfedgeDS_min_items.h>
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/HalfedgeDS_decorator.h>
+#include <cassert>
 
 // An items type using a halfedge with previous-pointer.
 struct My_items : public CGAL::HalfedgeDS_min_items {
@@ -22,6 +23,6 @@ int main() {
     HDS hds;
     Decorator decorator(hds);
     decorator.create_loop();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     return 0;
 }
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_halfedge_iterator.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_halfedge_iterator.cpp
index f1aea66723c..f81b87be6ee 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_halfedge_iterator.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_halfedge_iterator.cpp
@@ -1,5 +1,6 @@
 #include <CGAL/HalfedgeDS_default.h>
 #include <CGAL/HalfedgeDS_decorator.h>
+#include <cassert>
 
 struct Traits { typedef int Point_2; };
 typedef CGAL::HalfedgeDS_default<Traits> HDS;
@@ -11,10 +12,10 @@ int main() {
     Decorator decorator(hds);
     decorator.create_loop();
     decorator.create_segment();
-    CGAL_assertion( decorator.is_valid());
+    assert( decorator.is_valid());
     int n = 0;
     for ( Iterator i = hds.halfedges_begin(); i != hds.halfedges_end(); ++i )
         ++n;
-    CGAL_assertion( n == 4);  // == 2 edges
+    assert( n == 4);  // == 2 edges
     return 0;
 }
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp
index d87fd6bd85c..134092b3fba 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex.cpp
@@ -8,6 +8,7 @@
 #include <CGAL/make_mesh_3.h>
 
 #include <cstdlib>
+#include <cassert>
 
 // Domain
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
@@ -54,8 +55,7 @@ const std::pair<int, int> incident_subdomains[] = {
 int main()
 {
   const std::size_t nb_patches = sizeof(filenames) / sizeof(const char*);
-  CGAL_assertion(sizeof(incident_subdomains) ==
-                 nb_patches * sizeof(std::pair<int, int>));
+  assert(sizeof(incident_subdomains) == nb_patches * sizeof(std::pair<int, int>));
   std::vector<Polyhedron> patches(nb_patches);
   for(std::size_t i = 0; i < nb_patches; ++i) {
     std::ifstream input(CGAL::data_file_path(filenames[i]));
diff --git a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp
index 025870f6cbc..d6e2a8d8a89 100644
--- a/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_polyhedral_complex_sm.cpp
@@ -9,6 +9,7 @@
 #include <CGAL/Polyhedral_complex_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <cstdlib>
+#include <cassert>
 
 // Domain
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
@@ -63,8 +64,8 @@ int main()
 #endif
 
   const std::size_t nb_patches = sizeof(filenames) / sizeof(const char*);
-  CGAL_assertion(sizeof(incident_subdomains) ==
-                 nb_patches * sizeof(std::pair<int, int>));
+  assert(sizeof(incident_subdomains) ==
+	 nb_patches * sizeof(std::pair<int, int>));
   std::vector<Face_graph> patches(nb_patches);
   for(std::size_t i = 0; i < nb_patches; ++i) {
     std::ifstream input(CGAL::data_file_path(filenames[i]));
diff --git a/Nef_2/examples/Nef_2/nef_2_construction.cpp b/Nef_2/examples/Nef_2/nef_2_construction.cpp
index 903bee5bf28..cb434cf297f 100644
--- a/Nef_2/examples/Nef_2/nef_2_construction.cpp
+++ b/Nef_2/examples/Nef_2/nef_2_construction.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Filtered_extended_homogeneous.h>
 #include <CGAL/Nef_polyhedron_2.h>
+#include <cassert>
 
 typedef CGAL::Exact_integer RT;
 typedef CGAL::Filtered_extended_homogeneous<RT> Extended_kernel;
@@ -15,13 +16,13 @@ int main() {
   Line l(2,4,2); // l : 2x + 4y + 2 = 0
   Nef_polyhedron N2(l,Nef_polyhedron::INCLUDED);
   Nef_polyhedron N3 = N2.complement();
-  CGAL_assertion(N1 == N2.join(N3));
+  assert(N1 == N2.join(N3));
 
   Point p1(0,0), p2(10,10), p3(-20,15);
   Point triangle[3] = { p1, p2, p3 };
   Nef_polyhedron N4(triangle, triangle+3);
   Nef_polyhedron N5 = N2.intersection(N4);
-  CGAL_assertion(N5 <= N2 && N5 <= N4);
+  assert(N5 <= N2 && N5 <= N4);
 
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/comparison.cpp b/Nef_3/examples/Nef_3/comparison.cpp
index 79dceebb052..f6c5c40c474 100644
--- a/Nef_3/examples/Nef_3/comparison.cpp
+++ b/Nef_3/examples/Nef_3/comparison.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Extended_homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
+#include <cassert>
 
 typedef CGAL::Exact_integer  NT;
 typedef CGAL::Extended_homogeneous<NT>  Kernel;
@@ -12,16 +13,16 @@ int main() {
   Nef_polyhedron N1(Plane_3(2,5,7,11), Nef_polyhedron::INCLUDED);
   Nef_polyhedron N2(Plane_3(2,5,7,11), Nef_polyhedron::EXCLUDED);
 
-  CGAL_assertion(N1 >= N2);
-  CGAL_assertion(N2 <= N1);
-  CGAL_assertion(N1 != N2);
-  CGAL_assertion(N1 > N2);
-  CGAL_assertion(N2 < N1);
+  assert(N1 >= N2);
+  assert(N2 <= N1);
+  assert(N1 != N2);
+  assert(N1 > N2);
+  assert(N2 < N1);
 
   N2 = N2.closure();
-  CGAL_assertion(N1==N2);
-  CGAL_assertion(N1>=N2);
-  CGAL_assertion(N1<=N2);
+  assert(N1==N2);
+  assert(N1>=N2);
+  assert(N1<=N2);
 
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/nef_3_construction.cpp b/Nef_3/examples/Nef_3/nef_3_construction.cpp
index c70a1d5dae9..043f8ca8bdc 100644
--- a/Nef_3/examples/Nef_3/nef_3_construction.cpp
+++ b/Nef_3/examples/Nef_3/nef_3_construction.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Extended_homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
+#include <cassert>
 
 typedef CGAL::Extended_homogeneous<CGAL::Exact_integer>  Kernel;
 typedef CGAL::Nef_polyhedron_3<Kernel>  Nef_polyhedron;
@@ -14,19 +15,19 @@ int main() {
   Nef_polyhedron N4(Plane_3( 1, 2, 5,-1), Nef_polyhedron::INCLUDED);
   Nef_polyhedron N5(Plane_3( 1, 2, 5,-1), Nef_polyhedron::EXCLUDED);
 
-  CGAL_assertion(N0 == N1);
-  CGAL_assertion(N3 == N4);
-  CGAL_assertion(N0 != N2);
-  CGAL_assertion(N3 != N5);
+  assert(N0 == N1);
+  assert(N3 == N4);
+  assert(N0 != N2);
+  assert(N3 != N5);
 
-  CGAL_assertion(N4 >= N5);
-  CGAL_assertion(N5 <= N4);
-  CGAL_assertion(N4 > N5);
-  CGAL_assertion(N5 < N4);
+  assert(N4 >= N5);
+  assert(N5 <= N4);
+  assert(N4 > N5);
+  assert(N5 < N4);
 
   N5 = N5.closure();
-  CGAL_assertion(N4 >= N5);
-  CGAL_assertion(N4 <= N5);
+  assert(N4 >= N5);
+  assert(N4 <= N5);
 
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/nef_3_simple.cpp b/Nef_3/examples/Nef_3/nef_3_simple.cpp
index 5902ad85b20..bd9c1b2099b 100644
--- a/Nef_3/examples/Nef_3/nef_3_simple.cpp
+++ b/Nef_3/examples/Nef_3/nef_3_simple.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
+#include <cassert>
 
 typedef CGAL::Homogeneous<CGAL::Exact_integer>  Kernel;
 typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;
@@ -9,7 +10,7 @@ int main() {
   Nef_polyhedron N0(Nef_polyhedron::EMPTY);
   Nef_polyhedron N1(Nef_polyhedron::COMPLETE);
 
-  CGAL_assertion (N0 == N1.complement());
-  CGAL_assertion (N0 != N1);
+  assert(N0 == N1.complement());
+  assert(N0 != N1);
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/point_set_operations.cpp b/Nef_3/examples/Nef_3/point_set_operations.cpp
index 210ea348cef..82f09cd177d 100644
--- a/Nef_3/examples/Nef_3/point_set_operations.cpp
+++ b/Nef_3/examples/Nef_3/point_set_operations.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Extended_homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
+#include <cassert>
 
 typedef CGAL::Extended_homogeneous<CGAL::Exact_integer>  Kernel;
 typedef CGAL::Nef_polyhedron_3<Kernel>  Nef_polyhedron;
@@ -22,11 +23,11 @@ int main() {
   Cube1 *= !I3;
   Nef_polyhedron Cube2 = N1 * N2 * N3 * N4 * N5 * N6;
 
-  CGAL_assertion(Cube1 == Cube2);  // both are closed cube
-  CGAL_assertion(Cube1 == Cube1.closure());
-  CGAL_assertion(Cube1 == Cube1.regularization());
-  CGAL_assertion((N1 - N1.boundary()) == N1.interior());
-  CGAL_assertion(I1.closure() == I1.complement().interior().complement());
-  CGAL_assertion(I1.regularization() == I1.interior().closure());
+  assert(Cube1 == Cube2);  // both are closed cube
+  assert(Cube1 == Cube1.closure());
+  assert(Cube1 == Cube1.regularization());
+  assert((N1 - N1.boundary()) == N1.interior());
+  assert(I1.closure() == I1.complement().interior().complement());
+  assert(I1.regularization() == I1.interior().closure());
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/set_operations.cpp b/Nef_3/examples/Nef_3/set_operations.cpp
index 5efa840cf8e..93a9ac78a96 100644
--- a/Nef_3/examples/Nef_3/set_operations.cpp
+++ b/Nef_3/examples/Nef_3/set_operations.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Extended_homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
+#include <cassert>
 
 typedef CGAL::Exact_integer  NT;
 typedef CGAL::Extended_homogeneous<NT>  Kernel;
@@ -22,6 +23,6 @@ int main() {
   Nef_polyhedron Cube1(I2 *!I1);
   Cube1 *= !I3;
   Nef_polyhedron Cube2 = N1 * N2 * N3 * N4 * N5 * N6;
-  CGAL_assertion (Cube1 == Cube2);
+  assert(Cube1 == Cube2);
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/topological_operations.cpp b/Nef_3/examples/Nef_3/topological_operations.cpp
index 087d37b4418..d42d7210658 100644
--- a/Nef_3/examples/Nef_3/topological_operations.cpp
+++ b/Nef_3/examples/Nef_3/topological_operations.cpp
@@ -2,6 +2,7 @@
 #include <CGAL/Homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
 #include <CGAL/IO/Nef_polyhedron_iostream_3.h>
+#include <cassert>
 
 typedef CGAL::Exact_integer  NT;
 typedef CGAL::Homogeneous<NT>  Kernel;
@@ -12,9 +13,9 @@ int main() {
   Nef_polyhedron N;
   std::cin >> N;
 
-  CGAL_assertion((N - N.boundary()) == N.interior());
-  CGAL_assertion(N.closure() == N.complement().interior().complement());
-  CGAL_assertion(N.regularization() == N.interior().closure());
+  assert((N - N.boundary()) == N.interior());
+  assert(N.closure() == N.complement().interior().complement());
+  assert(N.regularization() == N.interior().closure());
 
   return 0;
 }
diff --git a/Nef_3/examples/Nef_3/transformation.cpp b/Nef_3/examples/Nef_3/transformation.cpp
index 0e79e62e832..a69de27ee48 100644
--- a/Nef_3/examples/Nef_3/transformation.cpp
+++ b/Nef_3/examples/Nef_3/transformation.cpp
@@ -2,6 +2,7 @@
 #include <CGAL/Extended_homogeneous.h>
 #include <CGAL/Nef_polyhedron_3.h>
 #include <CGAL/IO/Nef_polyhedron_iostream_3.h>
+#include <cassert>
 
 
 typedef CGAL::Extended_homogeneous<CGAL::Exact_integer>  Kernel;
@@ -21,11 +22,11 @@ int main() {
   Aff_transformation_3 scale(CGAL::SCALING, 3, 2);
 
   N.transform(transl);
-  CGAL_assertion(N == Nef_polyhedron(Plane_3(0,1,0,-7)));
+  assert(N == Nef_polyhedron(Plane_3(0,1,0,-7)));
   N.transform(rotx90);
-  CGAL_assertion(N == Nef_polyhedron(Plane_3(0,0,1,-7)));
+  assert(N == Nef_polyhedron(Plane_3(0,0,1,-7)));
   N.transform(scale);
-  CGAL_assertion(N == Nef_polyhedron(Plane_3(0,0,2,-21)));
+  assert(N == Nef_polyhedron(Plane_3(0,0,2,-21)));
 
   return 0;
 }
diff --git a/Nef_S2/examples/Nef_S2/nef_s2_construction.cpp b/Nef_S2/examples/Nef_S2/nef_s2_construction.cpp
index 679f5f0b4bf..e0c28b413e0 100644
--- a/Nef_S2/examples/Nef_S2/nef_s2_construction.cpp
+++ b/Nef_S2/examples/Nef_S2/nef_s2_construction.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Exact_integer.h>
 #include <CGAL/Homogeneous.h>
 #include <CGAL/Nef_polyhedron_S2.h>
+#include <cassert>
 
 typedef CGAL::Exact_integer RT;
 typedef CGAL::Homogeneous<RT> Kernel;
@@ -16,7 +17,7 @@ int main() {
   Sphere_circle c(1,1,1); // c : x + y + z = 0
   Nef_polyhedron N2(c, Nef_polyhedron::INCLUDED);
   Nef_polyhedron N3(N2.complement());
-  CGAL_assertion(N1 == N2.join(N3));
+  assert(N1 == N2.join(N3));
   Sphere_point   p1(1,0,0), p2(0,1,0), p3(0,0,1);
   Sphere_segment s1(p1,p2), s2(p2,p3), s3(p3,p1);
   Sphere_segment triangle[3] = { s1, s2, s3 };
@@ -24,7 +25,7 @@ int main() {
   Nef_polyhedron N5;
   N5 += N2;
   N5 = N5.intersection(N4);
-  CGAL_assertion(N5 <= N2 && N5 != N4);
+  assert(N5 <= N2 && N5 != N4);
 
   return 0;
 }
diff --git a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp
index c99cf2361d0..11bbef2e0f4 100644
--- a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp
+++ b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/draw_periodic_2_triangulation_2.cpp
@@ -23,7 +23,6 @@ int main(int argc, char* argv[])
   {
     while (ifs >> p)
     { T.insert(p); }
-    CGAL_assertion(T.is_valid());
 
     if( T.is_triangulation_in_1_sheet())
     { T.convert_to_9_sheeted_covering(); }
diff --git a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_pair_iterator_2.cpp b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_pair_iterator_2.cpp
index 921afdc0bd1..3a18d93e99d 100644
--- a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_pair_iterator_2.cpp
+++ b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_pair_iterator_2.cpp
@@ -31,8 +31,6 @@ int main()
   Delaunay T;
   T.insert( points.begin(), points.end() );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   Delaunay::Finite_vertices_iterator vit;
   for (vit = T.finite_vertices_begin(); vit != T.finite_vertices_end(); ++vit)
diff --git a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_transform_iterator_2.cpp b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_transform_iterator_2.cpp
index c67bf9f324c..e416be8bf4f 100644
--- a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_transform_iterator_2.cpp
+++ b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_transform_iterator_2.cpp
@@ -46,8 +46,6 @@ int main()
   T.insert( boost::make_transform_iterator(points.begin(), Auto_count()),
             boost::make_transform_iterator(points.end(),  Auto_count() )  );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   Delaunay::Finite_vertices_iterator vit;
   for (vit = T.finite_vertices_begin(); vit != T.finite_vertices_end(); ++vit)
diff --git a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_zip_iterator_2.cpp b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_zip_iterator_2.cpp
index 7862f102373..dabb31388a7 100644
--- a/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_zip_iterator_2.cpp
+++ b/Periodic_2_triangulation_2/examples/Periodic_2_triangulation_2/p2t2_info_insert_with_zip_iterator_2.cpp
@@ -41,9 +41,6 @@ int main()
   T.insert( boost::make_zip_iterator(boost::make_tuple( points.begin(), indices.begin() )),
             boost::make_zip_iterator(boost::make_tuple( points.end(), indices.end() ) )  );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
-
   // check that the info was correctly set.
   Delaunay::Finite_vertices_iterator vit;
   for (vit = T.finite_vertices_begin(); vit != T.finite_vertices_end(); ++vit)
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_OM.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_OM.cpp
index 1ebd95c650d..cc8dd4d54f4 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_OM.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/hole_filling_example_OM.cpp
@@ -10,6 +10,7 @@
 #include <iostream>
 #include <fstream>
 #include <vector>
+#include <cassert>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel   Kernel;
 
@@ -42,7 +43,7 @@ int main(int argc, char* argv[])
                                                                        CGAL::parameters::vertex_point_map(get(CGAL::vertex_point, mesh))
                                                                                         .geom_traits(Kernel())));
 
-      CGAL_assertion(CGAL::is_valid_polygon_mesh(mesh));
+      assert(CGAL::is_valid_polygon_mesh(mesh));
 
       std::cout << "* FILL HOLE NUMBER " << ++nb_holes << std::endl;
       std::cout << "  Number of facets in constructed patch: " << patch_facets.size() << std::endl;
@@ -51,7 +52,7 @@ int main(int argc, char* argv[])
     }
   }
 
-  CGAL_assertion(CGAL::is_valid_polygon_mesh(mesh));
+  assert(CGAL::is_valid_polygon_mesh(mesh));
   std::cout << std::endl;
   std::cout << nb_holes << " holes have been filled" << std::endl;
 
diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/triangulate_polyline_example.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/triangulate_polyline_example.cpp
index 204dd3e2ed5..5133aa1ffcc 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/triangulate_polyline_example.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/triangulate_polyline_example.cpp
@@ -5,6 +5,7 @@
 
 #include <vector>
 #include <iterator>
+#include <cassert>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
 typedef Kernel::Point_3                                     Point;
@@ -44,7 +45,7 @@ int main()
   std::vector<Triangle_int> patch_will_be_empty;
   CGAL::Polygon_mesh_processing::triangulate_hole_polyline(polyline_collinear,
                                                            back_inserter(patch_will_be_empty));
-  CGAL_assertion(patch_will_be_empty.empty());
+  assert(patch_will_be_empty.empty());
 
   return 0;
 }
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_incr_builder.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_incr_builder.cpp
index a5f62cce5a1..f43e5b4e6a8 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_incr_builder.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_incr_builder.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Polyhedron_incremental_builder_3.h>
 #include <CGAL/Polyhedron_3.h>
+#include <cassert>
 
 // A modifier creating a triangle with the incremental builder.
 template <class HDS>
@@ -33,6 +34,6 @@ int main() {
     Polyhedron P;
     Build_triangle<HalfedgeDS> triangle;
     P.delegate( triangle);
-    CGAL_assertion( P.is_triangle( P.halfedges_begin()));
+    assert( P.is_triangle( P.halfedges_begin()));
     return 0;
 }
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_off.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_off.cpp
index d1fdd179c41..ff7a3209571 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_off.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_off.cpp
@@ -26,7 +26,6 @@ int main() {
     for (  Facet_iterator i = P.facets_begin(); i != P.facets_end(); ++i) {
         Halfedge_facet_circulator j = i->facet_begin();
         // Facets in polyhedral surfaces are at least triangles.
-        CGAL_assertion( CGAL::circulator_size(j) >= 3);
         std::cout << CGAL::circulator_size(j) << ' ';
         do {
             std::cout << ' ' << std::distance(P.vertices_begin(), j->vertex());
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp
index 0a2c85b4c8c..e972a9f92d8 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv.cpp
@@ -5,6 +5,7 @@
 #include <vector>
 #include <cmath>
 #include <fstream>
+#include <cassert>
 
 typedef CGAL::Simple_cartesian<double>                       Kernel;
 typedef Kernel::Vector_3                                     Vector;
@@ -27,7 +28,7 @@ void create_center_vertex( Polyhedron& P, Facet_iterator f) {
         vec = vec + ( h->vertex()->point() - CGAL::ORIGIN);
         ++ order;
     } while ( ++h != f->facet_begin());
-    CGAL_assertion( order >= 3); // guaranteed by definition of polyhedron
+    assert( order >= 3); // guaranteed by definition of polyhedron
     Point center =  CGAL::ORIGIN + (vec / static_cast<double>(order));
     Halfedge_handle new_center = P.create_center_vertex( f->halfedge());
     new_center->vertex()->point() = center;
@@ -44,7 +45,7 @@ struct Smooth_old_vertex {
             vec = vec + ( h->opposite()->vertex()->point() - CGAL::ORIGIN)
               * alpha / static_cast<double>(degree);
             ++ h;
-            CGAL_assertion( h != v.vertex_begin()); // even degree guaranteed
+            assert( h != v.vertex_begin()); // even degree guaranteed
             ++ h;
         } while ( h != v.vertex_begin());
         return (CGAL::ORIGIN + vec);
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp
index f1d0de4f8f5..d8c7c05c2e5 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_prog_subdiv_with_boundary.cpp
@@ -7,6 +7,7 @@
 #include <cctype>
 #include <cmath>
 #include <fstream>
+#include <cassert>
 
 typedef CGAL::Simple_cartesian<double>                       Kernel;
 typedef Kernel::Vector_3                                     Vector;
@@ -29,7 +30,7 @@ void create_center_vertex( Polyhedron& P, Facet_iterator f) {
         vec = vec + ( h->vertex()->point() - CGAL::ORIGIN);
         ++ order;
     } while ( ++h != f->facet_begin());
-    CGAL_assertion( order >= 3); // guaranteed by definition of polyhedron
+    assert( order >= 3); // guaranteed by definition of polyhedron
     Point center =  CGAL::ORIGIN + (vec / static_cast<double>(order));
     Halfedge_handle new_center = P.create_center_vertex( f->halfedge());
     new_center->vertex()->point() = center;
@@ -55,7 +56,7 @@ struct Smooth_old_vertex {
             vec = vec + ( h->opposite()->vertex()->point() - CGAL::ORIGIN)
               * alpha / static_cast<double>(degree);
             ++ h;
-            CGAL_assertion( h != v.vertex_begin()); // even degree guaranteed
+            assert( h != v.vertex_begin()); // even degree guaranteed
             ++ h;
         } while ( h != v.vertex_begin());
         return (CGAL::ORIGIN + vec);
@@ -101,11 +102,10 @@ void subdiv( Polyhedron& P) {
         ++e; // careful, incr. before flip since flip destroys current edge
         flip_edge( P, h);
     };
-    CGAL_postcondition( P.is_valid());
 }
 
 void trisect_border_halfedge( Polyhedron& P, Halfedge_handle e) {
-    CGAL_precondition( e->is_border());
+    assert( e->is_border());
     // Create two new vertices on e.
     e = e->prev();
     P.split_vertex( e, e->next()->opposite());
@@ -121,7 +121,7 @@ void trisect_border_halfedge( Polyhedron& P, Halfedge_handle e) {
 
 template <class OutputIterator>
 void smooth_border_vertices( Halfedge_handle e, OutputIterator out) {
-    CGAL_precondition( e->is_border());
+    assert( e->is_border());
     // We know that the vertex at this edge is from the unrefined mesh.
     // Get the locus vectors of the unrefined vertices in the neighborhood.
     Vector v0 = e->prev()->prev()->opposite()->vertex()->point() -CGAL::ORIGIN;
@@ -166,8 +166,6 @@ void subdiv_border( Polyhedron& P) {
             e->next()->vertex()->point() = *i++;
         }
     } while ( e++ != last_e);
-    CGAL_assertion( i == pts.end());
-    CGAL_postcondition( P.is_valid());
 }
 
 using namespace std;
diff --git a/Polyhedron/examples/Polyhedron/polyhedron_self_intersection.cpp b/Polyhedron/examples/Polyhedron/polyhedron_self_intersection.cpp
index 4561bd14770..909531d09eb 100644
--- a/Polyhedron/examples/Polyhedron/polyhedron_self_intersection.cpp
+++ b/Polyhedron/examples/Polyhedron/polyhedron_self_intersection.cpp
@@ -6,6 +6,7 @@
 #include <algorithm>
 #include <vector>
 #include <fstream>
+#include <cassert>
 
 using std::cerr;
 using std::endl;
@@ -63,7 +64,7 @@ struct Intersect_facets {
         }
         if ( v != Halfedge_const_handle()) {
             // found shared vertex:
-            CGAL_assertion( h->vertex() == v->vertex());
+            assert( h->vertex() == v->vertex());
             // geomtric check if the opposite segments intersect the triangles
             Triangle t1( h->vertex()->point(),
                          h->next()->vertex()->point(),
diff --git a/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-exact-linf.cpp b/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-exact-linf.cpp
index 99f740e5110..7259ddd553e 100644
--- a/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-exact-linf.cpp
+++ b/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-exact-linf.cpp
@@ -35,8 +35,6 @@ int main( int argc, char *argv[] ) {
   // read the sites from the stream and insert them in the diagram
   while ( ifs >> site ) {
     sdg.insert( site );
-    CGAL_SDG_DEBUG( sdg.file_output_verbose(std::cout); );
-    CGAL_assertion( sdg.is_valid(false, 1) );
   }
 
   ifs.close();
diff --git a/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-linf.cpp b/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-linf.cpp
index 576f3fe4d4c..9a6fc350e19 100644
--- a/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-linf.cpp
+++ b/Segment_Delaunay_graph_Linf_2/examples/Segment_Delaunay_graph_Linf_2/sdg-voronoi-edges-linf.cpp
@@ -32,8 +32,6 @@ int main( int argc, char *argv[] ) {
   // read the sites from the stream and insert them in the diagram
   while ( ifs >> site ) {
     sdg.insert( site );
-    CGAL_SDG_DEBUG( sdg.file_output_verbose(std::cout); );
-    CGAL_assertion( sdg.is_valid(false, 1) );
   }
 
   ifs.close();
diff --git a/Stream_support/examples/Stream_support/iv2off.cpp b/Stream_support/examples/Stream_support/iv2off.cpp
index 231c7cff65d..676a6e56ac4 100644
--- a/Stream_support/examples/Stream_support/iv2off.cpp
+++ b/Stream_support/examples/Stream_support/iv2off.cpp
@@ -67,7 +67,6 @@ void iv_file_scanner( istream& in)
                         // point coordinate list starts here
                         offset = points.size();
                         in >> c;
-                        CGAL_assertion( c == '[');
                         in >> c;
                         while ( in && ( c != ']')) {
                             in.putback( c);
@@ -99,7 +98,6 @@ void iv_file_scanner( istream& in)
                     // indices start here
                     std::size_t face_offset = facets.size();
                     in >> c;
-                    CGAL_assertion( c == '[');
                     facets.push_back( Facet());
                     Facet* facet = &facets.back();
                     in >> c;
@@ -133,7 +131,6 @@ void iv_file_scanner( istream& in)
                     // indices start here
                     std::size_t face_offset = facets.size();
                     in >> c;
-                    CGAL_assertion( c == '[');
                     facets.push_back( Facet());
                     Facet* facet = &facets.back();
                     in >> c;
diff --git a/Surface_mesh/examples/Surface_mesh/draw_surface_mesh_small_faces.h b/Surface_mesh/examples/Surface_mesh/draw_surface_mesh_small_faces.h
index 0e5043c8f08..b8eeac5b008 100644
--- a/Surface_mesh/examples/Surface_mesh/draw_surface_mesh_small_faces.h
+++ b/Surface_mesh/examples/Surface_mesh/draw_surface_mesh_small_faces.h
@@ -20,6 +20,8 @@
 #include <CGAL/Surface_mesh.h>
 #include <CGAL/Random.h>
 
+#include <cassert>
+
 template<class SM>
 class SimpleSurfaceMeshWithSmallFacesViewerQt : public CGAL::Basic_viewer_qt
 {
@@ -54,7 +56,7 @@ public:
       bool exist;
       typename SM::template Property_map<face_descriptor, FT> faces_size;
       boost::tie(faces_size, exist)=sm.template property_map<face_descriptor, FT>("f:size");
-      CGAL_assertion(exist);
+      assert(exist);
 
       m_min_size=faces_size[*(sm.faces().begin())];
       m_max_size=m_min_size;
@@ -84,7 +86,7 @@ protected:
     bool exist;
     typename SM::template Property_map<face_descriptor, FT> faces_size;
     boost::tie(faces_size, exist)=sm.template property_map<face_descriptor, FT>("f:size");
-    CGAL_assertion(exist);
+    assert(exist);
 
     // It it is smaller, color the face in red.
     if (get(faces_size, fh)<m_min_size+((m_max_size-m_min_size)/(100-m_threshold)))
diff --git a/Surface_mesh/examples/Surface_mesh/sm_draw_small_faces.cpp b/Surface_mesh/examples/Surface_mesh/sm_draw_small_faces.cpp
index 7fd8165096d..5d6c3b3d54e 100644
--- a/Surface_mesh/examples/Surface_mesh/sm_draw_small_faces.cpp
+++ b/Surface_mesh/examples/Surface_mesh/sm_draw_small_faces.cpp
@@ -4,6 +4,7 @@
 #include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
 #include <fstream>
 #include <string>
+#include <cassert>
 #include "draw_surface_mesh_small_faces.h"
 
 typedef CGAL::Simple_cartesian<double> K;
@@ -28,7 +29,7 @@ int main(int argc, char* argv[])
   Mesh::Property_map<face_descriptor, FT> faces_size;
   bool created;
   boost::tie(faces_size, created)=sm.add_property_map<face_descriptor, FT>("f:size",0.);
-  CGAL_assertion(created);
+  assert(created);
 
   for(face_descriptor fd : sm.faces())
   { faces_size[fd]=CGAL::Polygon_mesh_processing::face_area(fd, sm); }
@@ -39,4 +40,3 @@ int main(int argc, char* argv[])
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h
index 7f020ae5c6a..36afb2b7419 100644
--- a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h
+++ b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_generate_input.h
@@ -14,6 +14,7 @@
 
 #include <boost/unordered_set.hpp>
 #include <utility>
+#include <cassert>
 
 namespace CGAL
 {
@@ -42,7 +43,7 @@ namespace Tetrahedral_remeshing
       else
         c->set_subdomain_index(2);
     }
-    CGAL_assertion(tr.is_valid(true));
+    assert(tr.is_valid(true));
   }
 
 
@@ -66,7 +67,7 @@ namespace Tetrahedral_remeshing
     for (typename Tr::Cell_handle c : tr.finite_cell_handles())
       c->set_subdomain_index(1);
 
-    CGAL_assertion(tr.is_valid(true));
+    assert(tr.is_valid(true));
   }
 
   template<typename Tr>
@@ -185,7 +186,7 @@ namespace Tetrahedral_remeshing
     add_edge(v2, v6, tr, constraints);
     add_edge(v3, v7, tr, constraints);
 
-    CGAL_assertion(tr.is_valid(true));
+    assert(tr.is_valid(true));
   }
 }
-}
\ No newline at end of file
+}
diff --git a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp
index 26c967e5f63..bc7504705d7 100644
--- a/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp
+++ b/Tetrahedral_remeshing/examples/Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp
@@ -9,6 +9,7 @@
 
 #include <iostream>
 #include <utility>
+#include <cassert>
 
 #include "tetrahedral_remeshing_generate_input.h"
 
@@ -45,8 +46,8 @@ public:
                   const key_type& k,
                   const bool b)
   {
-    CGAL_assertion(map.m_set_ptr != nullptr);
-    CGAL_assertion(k.first < k.second);
+    assert(map.m_set_ptr != nullptr);
+    assert(k.first < k.second);
     if (b)  map.m_set_ptr->insert(k);
     else    map.m_set_ptr->erase(k);
   }
@@ -54,8 +55,8 @@ public:
   friend value_type get(const Constrained_edges_property_map& map,
                         const key_type& k)
   {
-    CGAL_assertion(map.m_set_ptr != nullptr);
-    CGAL_assertion(k.first < k.second);
+    assert(map.m_set_ptr != nullptr);
+    assert(k.first < k.second);
     return (map.m_set_ptr->count(k) > 0);
   }
 };
@@ -80,7 +81,6 @@ int main(int argc, char* argv[])
 
   CGAL::Tetrahedral_remeshing::generate_input_cube(nbv, t3, constraints);
   make_constraints_from_cube_edges(t3, constraints);
-  CGAL_assertion(t3.is_valid());
 
   CGAL::tetrahedral_isotropic_remeshing(t3, target_edge_length,
     CGAL::parameters::edge_is_constrained_map(
@@ -89,4 +89,3 @@ int main(int argc, char* argv[])
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Triangulation_2/examples/Triangulation_2/copy_triangulation_2.cpp b/Triangulation_2/examples/Triangulation_2/copy_triangulation_2.cpp
index db1bd13ea3a..e757b35c7fb 100644
--- a/Triangulation_2/examples/Triangulation_2/copy_triangulation_2.cpp
+++ b/Triangulation_2/examples/Triangulation_2/copy_triangulation_2.cpp
@@ -3,6 +3,7 @@
 #include <CGAL/Delaunay_triangulation_2.h>
 
 #include <CGAL/point_generators_2.h>
+#include <cassert>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel EPIC;
 typedef CGAL::Exact_predicates_exact_constructions_kernel EPEC;
@@ -44,5 +45,5 @@ int main()
   dt2_epec.set_infinite_vertex(
     dt2_epec.tds().copy_tds( dt2_epic.tds(),dt2_epic.infinite_vertex(), Convert_vertex(), Convert_face() ) );
 
-  CGAL_assertion( dt2_epec.is_valid() );
+  assert( dt2_epec.is_valid() );
 }
diff --git a/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_2.cpp b/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_2.cpp
index 5d5f3620366..21d0df6bebd 100644
--- a/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_2.cpp
+++ b/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_2.cpp
@@ -24,8 +24,6 @@ int main()
   Delaunay T;
   T.insert( points.begin(),points.end() );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   Delaunay::Finite_vertices_iterator vit;
   for (Vertex_handle v : T.finite_vertex_handles())
diff --git a/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_regular_2.cpp b/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_regular_2.cpp
index 27b51dba0db..468b386d888 100644
--- a/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_regular_2.cpp
+++ b/Triangulation_2/examples/Triangulation_2/info_insert_with_pair_iterator_regular_2.cpp
@@ -28,8 +28,6 @@ int main()
   Regular rt;
   rt.insert( points.begin(),points.end() );
 
-  CGAL_assertion( rt.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   for (Vertex_handle v : rt.finite_vertex_handles())
     if( points[ v->info() ].first != v->point() ){
diff --git a/Triangulation_2/examples/Triangulation_2/info_insert_with_transform_iterator_2.cpp b/Triangulation_2/examples/Triangulation_2/info_insert_with_transform_iterator_2.cpp
index 5cf0f395c7a..13de245d23d 100644
--- a/Triangulation_2/examples/Triangulation_2/info_insert_with_transform_iterator_2.cpp
+++ b/Triangulation_2/examples/Triangulation_2/info_insert_with_transform_iterator_2.cpp
@@ -37,8 +37,6 @@ int main()
   T.insert( boost::make_transform_iterator(points.begin(),Auto_count()),
             boost::make_transform_iterator(points.end(),  Auto_count() )  );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   Delaunay::Finite_vertices_iterator vit;
   for (Vertex_handle v : T.finite_vertex_handles())
diff --git a/Triangulation_2/examples/Triangulation_2/info_insert_with_zip_iterator_2.cpp b/Triangulation_2/examples/Triangulation_2/info_insert_with_zip_iterator_2.cpp
index 27b0855a8c9..94059abb6f7 100644
--- a/Triangulation_2/examples/Triangulation_2/info_insert_with_zip_iterator_2.cpp
+++ b/Triangulation_2/examples/Triangulation_2/info_insert_with_zip_iterator_2.cpp
@@ -36,9 +36,6 @@ int main()
   T.insert( boost::make_zip_iterator(boost::make_tuple( points.begin(),indices.begin() )),
             boost::make_zip_iterator(boost::make_tuple( points.end(),indices.end() ) )  );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
-
   // check that the info was correctly set.
 
   for (Vertex_handle v : T.finite_vertex_handles())
diff --git a/Triangulation_3/examples/Triangulation_3/copy_triangulation_3.cpp b/Triangulation_3/examples/Triangulation_3/copy_triangulation_3.cpp
index 2915dc1ef6c..ab7e2c42458 100644
--- a/Triangulation_3/examples/Triangulation_3/copy_triangulation_3.cpp
+++ b/Triangulation_3/examples/Triangulation_3/copy_triangulation_3.cpp
@@ -3,6 +3,7 @@
 #include <CGAL/Delaunay_triangulation_3.h>
 
 #include <CGAL/point_generators_3.h>
+#include <cassert>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel EPIC;
 typedef CGAL::Exact_predicates_exact_constructions_kernel EPEC;
@@ -43,5 +44,5 @@ int main()
   dt3_epec.set_infinite_vertex(
     dt3_epec.tds().copy_tds( dt3_epic.tds(),dt3_epic.infinite_vertex(), Convert_vertex(), Convert_cell() ) );
 
-  CGAL_assertion( dt3_epec.is_valid() );
+  assert( dt3_epec.is_valid() );
 }
diff --git a/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator.cpp b/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator.cpp
index 0b9c8a44100..8e089f0c368 100644
--- a/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator.cpp
+++ b/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator.cpp
@@ -26,8 +26,6 @@ int main()
 
   Delaunay T( points.begin(),points.end() );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   for (Delaunay::Vertex_handle v : T.finite_vertex_handles())
     if( points[ v->info() ].first != v->point() ){
diff --git a/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator_regular.cpp b/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator_regular.cpp
index 63d68a3e20a..ec51d80a277 100644
--- a/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator_regular.cpp
+++ b/Triangulation_3/examples/Triangulation_3/info_insert_with_pair_iterator_regular.cpp
@@ -26,8 +26,6 @@ int main()
 
   Regular rt( points.begin(),points.end() );
 
-  CGAL_assertion( rt.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   for (Regular::Vertex_handle v : rt.finite_vertex_handles())
     if( points[ v->info() ].first != v->point() ){
diff --git a/Triangulation_3/examples/Triangulation_3/info_insert_with_transform_iterator.cpp b/Triangulation_3/examples/Triangulation_3/info_insert_with_transform_iterator.cpp
index b28d792f3d4..9c673471bc9 100644
--- a/Triangulation_3/examples/Triangulation_3/info_insert_with_transform_iterator.cpp
+++ b/Triangulation_3/examples/Triangulation_3/info_insert_with_transform_iterator.cpp
@@ -38,8 +38,6 @@ int main()
   Delaunay T( boost::make_transform_iterator(points.begin(),Auto_count()),
               boost::make_transform_iterator(points.end(),  Auto_count() )  );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   for (Delaunay::Vertex_handle v : T.finite_vertex_handles())
     if( points[ v->info() ] != v->point() ){
diff --git a/Triangulation_3/examples/Triangulation_3/info_insert_with_zip_iterator.cpp b/Triangulation_3/examples/Triangulation_3/info_insert_with_zip_iterator.cpp
index bf3a5988f30..ba8eb60b2f8 100644
--- a/Triangulation_3/examples/Triangulation_3/info_insert_with_zip_iterator.cpp
+++ b/Triangulation_3/examples/Triangulation_3/info_insert_with_zip_iterator.cpp
@@ -37,8 +37,6 @@ int main()
   Delaunay T( boost::make_zip_iterator(boost::make_tuple( points.begin(),indices.begin() )),
               boost::make_zip_iterator(boost::make_tuple( points.end(),indices.end() ) )  );
 
-  CGAL_assertion( T.number_of_vertices() == 6 );
-
   // check that the info was correctly set.
   for (Delaunay::Vertex_handle v : T.finite_vertex_handles() )
     if( points[ v->info() ] != v->point() ){