diff --git a/Combinatorial_map/examples/Combinatorial_map/map_3_operations.cpp b/Combinatorial_map/examples/Combinatorial_map/map_3_operations.cpp
index cf96103b56a..2949da9b484 100644
--- a/Combinatorial_map/examples/Combinatorial_map/map_3_operations.cpp
+++ b/Combinatorial_map/examples/Combinatorial_map/map_3_operations.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Combinatorial_map.h>
 #include <iostream>
 #include <cstdlib>
+#include <cassert>
 
 typedef CGAL::Combinatorial_map<3> CMap_3;
 typedef CMap_3::Dart_handle        Dart_handle;
@@ -13,19 +14,19 @@ int main()
   Dart_handle dh1 = cm.make_combinatorial_hexahedron();
 
   // Add two edges along two opposite facets.
-  CGAL_assertion( cm.is_insertable_cell_1_in_cell_2
-                        (cm.beta(dh1,1),cm.beta(dh1,0)) );
+  assert( cm.is_insertable_cell_1_in_cell_2
+	  (cm.beta(dh1,1),cm.beta(dh1,0)) );
 
   cm.insert_cell_1_in_cell_2(cm.beta(dh1,1), cm.beta(dh1,0));
-  CGAL_assertion( cm.is_valid() );
+  assert( cm.is_valid() );
 
   Dart_handle dh2=cm.beta(dh1,2,1,1,2);
 
-  CGAL_assertion( cm.is_insertable_cell_1_in_cell_2
-                              (dh2,cm.beta(dh2,1,1)) );
+  assert( cm.is_insertable_cell_1_in_cell_2
+	  (dh2,cm.beta(dh2,1,1)) );
 
   cm.insert_cell_1_in_cell_2(dh2, cm.beta(dh2,1,1));
-  CGAL_assertion( cm.is_valid() );
+  assert( cm.is_valid() );
 
   // Insert a facet along these two new edges plus two initial edges
   // of the hexahedron.
@@ -35,28 +36,28 @@ int main()
   path.push_back(cm.beta(dh2,0));
   path.push_back(cm.beta(dh2,2,1));
 
-  CGAL_assertion( (cm.is_insertable_cell_2_in_cell_3
+  assert( (cm.is_insertable_cell_2_in_cell_3
                                (path.begin(),path.end())) );
 
   Dart_handle dh3=cm.insert_cell_2_in_cell_3(path.begin(),path.end());
-  CGAL_assertion( cm.is_valid() );
+  assert( cm.is_valid() );
 
   // Display the combinatorial map characteristics.
   cm.display_characteristics(std::cout) << ", valid=" <<
     cm.is_valid() << std::endl;
 
   // We use the removal operations to get back to the initial hexahedron.
-  CGAL_assertion( (cm.is_removable<2>(dh3)) );
+  assert( (cm.is_removable<2>(dh3)) );
   cm.remove_cell<2>(dh3);
-  CGAL_assertion( cm.is_valid() );
+  assert( cm.is_valid() );
 
-  CGAL_assertion( (cm.is_removable<1>(cm.beta(dh1,1))) );
+  assert( (cm.is_removable<1>(cm.beta(dh1,1))) );
   cm.remove_cell<1>(cm.beta(dh1,1));
-  CGAL_assertion( cm.is_valid() );
+  assert( cm.is_valid() );
 
-  CGAL_assertion( (cm.is_removable<1>(cm.beta(dh2,0))) );
+  assert( (cm.is_removable<1>(cm.beta(dh2,0))) );
   cm.remove_cell<1>(cm.beta(dh2,0));
-  CGAL_assertion( cm.is_valid() );
+  assert( cm.is_valid() );
 
   // Display the combinatorial map characteristics.
   cm.display_characteristics(std::cout) << ", valid="
@@ -64,4 +65,3 @@ int main()
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Generalized_map/examples/Generalized_map/gmap_3_marks.cpp b/Generalized_map/examples/Generalized_map/gmap_3_marks.cpp
index a0d3acb288d..e87b9413fbd 100644
--- a/Generalized_map/examples/Generalized_map/gmap_3_marks.cpp
+++ b/Generalized_map/examples/Generalized_map/gmap_3_marks.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Generalized_map.h>
 #include <iostream>
 #include <cstdlib>
+#include <cassert>
 
 typedef CGAL::Generalized_map<3> GMap_3;
 typedef GMap_3::Dart_handle Dart_handle;
@@ -26,9 +27,9 @@ int main()
   Dart_handle dh1 = gm.make_combinatorial_tetrahedron();
   Dart_handle dh2 = gm.make_combinatorial_tetrahedron();
 
-  CGAL_assertion( gm.is_valid() );
-  CGAL_assertion( gm.is_volume_combinatorial_tetrahedron(dh1) );
-  CGAL_assertion( gm.is_volume_combinatorial_tetrahedron(dh2) );
+  assert( gm.is_valid() );
+  assert( gm.is_volume_combinatorial_tetrahedron(dh1) );
+  assert( gm.is_volume_combinatorial_tetrahedron(dh2) );
 
   // 3) 3-sew them.
   gm.sew<3>(dh1, dh2);
@@ -59,4 +60,3 @@ int main()
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Generalized_map/examples/Generalized_map/gmap_3_operations.cpp b/Generalized_map/examples/Generalized_map/gmap_3_operations.cpp
index 9c3050d6dbd..7b99b1838f2 100644
--- a/Generalized_map/examples/Generalized_map/gmap_3_operations.cpp
+++ b/Generalized_map/examples/Generalized_map/gmap_3_operations.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Generalized_map.h>
 #include <iostream>
 #include <cstdlib>
+#include <cassert>
 
 typedef CGAL::Generalized_map<3> GMap_3;
 typedef GMap_3::Dart_handle      Dart_handle;
@@ -14,11 +15,11 @@ int main()
 
   // Add two edges along two opposite facets.
   gm.insert_cell_1_in_cell_2(d1,gm.alpha<0,1,0>(d1));
-  CGAL_assertion( gm.is_valid() );
+  assert( gm.is_valid() );
 
   Dart_handle d2=gm.alpha<2,1,0,1,2>(d1);
   gm.insert_cell_1_in_cell_2(d2,gm.alpha<0,1,0>(d2));
-  CGAL_assertion( gm.is_valid() );
+  assert( gm.is_valid() );
 
   // Insert a facet along these two new edges plus two initial edges
   // of the hexahedron.
@@ -29,7 +30,7 @@ int main()
   path.push_back(gm.alpha<2,1>(d2));
 
   Dart_handle d3=gm.insert_cell_2_in_cell_3(path.begin(),path.end());
-  CGAL_assertion( gm.is_valid() );
+  assert( gm.is_valid() );
 
   // Display the generalized map characteristics.
   gm.display_characteristics(std::cout) << ", valid=" <<
@@ -37,14 +38,14 @@ int main()
 
    // We use the removal operations to get back to the initial hexahedron.
   gm.remove_cell<2>(d3);
-  CGAL_assertion( gm.is_valid() );
+  assert( gm.is_valid() );
 
   gm.remove_cell<1>(gm.alpha<1>(d1));
-  CGAL_assertion( gm.is_valid() );
+  assert( gm.is_valid() );
 
   gm.remove_cell<1>(gm.alpha<1>(d2));
-  CGAL_assertion( gm.is_valid() );
-  CGAL_assertion( gm.is_volume_combinatorial_hexahedron(d1) );
+  assert( gm.is_valid() );
+  assert( gm.is_volume_combinatorial_hexahedron(d1) );
 
   // Display the generalized map characteristics.
   gm.display_characteristics(std::cout) << ", valid="
@@ -52,4 +53,3 @@ int main()
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Generalized_map/examples/Generalized_map/gmap_4_simple_example.cpp b/Generalized_map/examples/Generalized_map/gmap_4_simple_example.cpp
index e447da890e0..0f31affd7e0 100644
--- a/Generalized_map/examples/Generalized_map/gmap_4_simple_example.cpp
+++ b/Generalized_map/examples/Generalized_map/gmap_4_simple_example.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Generalized_map.h>
 #include <iostream>
 #include <cstdlib>
+#include <cassert>
 
 typedef CGAL::Generalized_map<4> GMap_4;
 typedef GMap_4::Dart_handle Dart_handle;
@@ -11,7 +12,7 @@ int main()
   Dart_handle d1 = gm.make_combinatorial_tetrahedron();
   Dart_handle d2 = gm.make_combinatorial_tetrahedron();
 
-  CGAL_assertion(gm.is_valid());
+  assert(gm.is_valid());
 
   gm.sew<4>(d1,d2);
 
diff --git a/HalfedgeDS/examples/HalfedgeDS/hds_prog_vector.cpp b/HalfedgeDS/examples/HalfedgeDS/hds_prog_vector.cpp
index 6e7fab933bb..9843c8199cc 100644
--- a/HalfedgeDS/examples/HalfedgeDS/hds_prog_vector.cpp
+++ b/HalfedgeDS/examples/HalfedgeDS/hds_prog_vector.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/HalfedgeDS_items_2.h>
 #include <CGAL/HalfedgeDS_vector.h>
 #include <CGAL/HalfedgeDS_decorator.h>
+#include <cassert>
 
 struct Traits { typedef int Point_2; };
 typedef CGAL::HalfedgeDS_vector< Traits, CGAL::HalfedgeDS_items_2> HDS;
@@ -10,6 +11,6 @@ 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/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp
index c912b78abb2..e83e81fb878 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_4.cpp
@@ -1,6 +1,7 @@
 #include <CGAL/Linear_cell_complex_for_generalized_map.h>
 #include <iostream>
 #include <vector>
+#include <cassert>
 
 typedef CGAL::Linear_cell_complex_for_generalized_map<4,5> LCC_4;
 typedef LCC_4::Dart_handle                                 Dart_handle;
@@ -42,24 +43,24 @@ int main()
 
   // Add one vertex on the middle of the edge containing dart d1.
   Dart_handle d3 = lcc.insert_barycenter_in_cell<1>(d1);
-  CGAL_assertion( lcc.is_valid() );
+  assert( lcc.is_valid() );
 
   lcc.display_characteristics(std::cout);
   std::cout<<", valid="<<lcc.is_valid()<<std::endl;
 
   // Add one edge to cut the face containing dart d3 in two.
   Dart_handle d4 = lcc.insert_cell_1_in_cell_2(d3, lcc.alpha(d1, 1, 0, 1));
-  CGAL_assertion( lcc.is_valid() );
+  assert( lcc.is_valid() );
 
   lcc.display_characteristics(std::cout);
   std::cout<<", valid="<<lcc.is_valid()<<std::endl;
 
   // We use removal operations to get back to the initial configuration.
   lcc.remove_cell<1>(d4);
-  CGAL_assertion( lcc.is_valid() );
+  assert( lcc.is_valid() );
 
   lcc.remove_cell<0>(d3);
-  CGAL_assertion( lcc.is_valid() );
+  assert( lcc.is_valid() );
 
   lcc.unsew<4>(d1);
 
@@ -68,4 +69,3 @@ int main()
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/voronoi_2.cpp b/Linear_cell_complex/examples/Linear_cell_complex/voronoi_2.cpp
index 0e29564d815..ecf2d40d787 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/voronoi_2.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/voronoi_2.cpp
@@ -5,6 +5,7 @@
 
 #include <iostream>
 #include <fstream>
+#include <cassert>
 
 
 // This example works both with cmap and gmap as combinatorial data structure.
@@ -46,7 +47,7 @@ void display_voronoi(LCC_2& alcc, Dart_handle adart)
     toremove.pop();
   }
 
-  CGAL_assertion(alcc.is_without_boundary(1));
+  assert(alcc.is_without_boundary(1));
 
   std::cout<<"Voronoi subdvision, only finite faces:"<<std::endl<<"  ";
   alcc.display_characteristics(std::cout) << ", valid="
@@ -122,7 +123,7 @@ int main(int narg, char** argv)
 
   std::istream_iterator<Point> begin(iFile), end;
   T.insert(begin, end);
-  CGAL_assertion(T.is_valid(false));
+  assert(T.is_valid(false));
 
   // 2) Convert the triangulation into a 2D lcc.
   LCC_2 lcc;
@@ -131,7 +132,7 @@ int main(int narg, char** argv)
 
   Dart_handle dh=CGAL::import_from_triangulation_2<LCC_2, Triangulation>
     (lcc, T, &face_to_dart);
-  CGAL_assertion(lcc.is_without_boundary());
+  assert(lcc.is_without_boundary());
 
   std::cout<<"Delaunay triangulation :"<<std::endl<<"  ";
   lcc.display_characteristics(std::cout) << ", valid="
@@ -141,7 +142,7 @@ int main(int narg, char** argv)
   LCC_2 dual_lcc;
   Dart_handle ddh=lcc.dual(dual_lcc, dh);
   // Here, dual_lcc is the 2D Voronoi diagram.
-  CGAL_assertion(dual_lcc.is_without_boundary());
+  assert(dual_lcc.is_without_boundary());
 
   // 4) We update the geometry of dual_lcc by using the std::map
   //    face_to_dart.
@@ -159,4 +160,3 @@ int main(int narg, char** argv)
 
   return EXIT_SUCCESS;
 }
-
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp b/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp
index bb22f59c2dc..b19be33520c 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/voronoi_3.cpp
@@ -4,6 +4,7 @@
 
 #include <iostream>
 #include <fstream>
+#include <cassert>
 
 /* // If you want to use exact constructions.
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
@@ -48,7 +49,7 @@ void display_voronoi(LCC_3& alcc, Dart_handle adart)
     toremove.pop();
   }
 
-  CGAL_assertion(alcc.is_without_boundary(1) && alcc.is_without_boundary(2));
+  assert(alcc.is_without_boundary(1) && alcc.is_without_boundary(2));
 
   std::cout<<"Voronoi subdvision, only finite volumes:"<<std::endl<<"  ";
   alcc.display_characteristics(std::cout) << ", valid="
@@ -126,7 +127,7 @@ int main(int narg, char** argv)
 
   std::istream_iterator<Point> begin(iFile), end;
   T.insert(begin, end);
-  CGAL_assertion(T.is_valid(false));
+  assert(T.is_valid(false));
 
   // 2) Convert the triangulation into a 3D lcc.
   LCC_3 lcc;
@@ -144,7 +145,7 @@ int main(int narg, char** argv)
   LCC_3 dual_lcc;
   Dart_handle ddh=lcc.dual(dual_lcc, dh);
   // Here, dual_lcc is the 3D Voronoi diagram.
-  CGAL_assertion(dual_lcc.is_without_boundary());
+  assert(dual_lcc.is_without_boundary());
 
   // 4) We update the geometry of dual_lcc by using the std::map
   //    face_to_dart.
@@ -161,4 +162,3 @@ int main(int narg, char** argv)
 
   return EXIT_SUCCESS;
 }
-