diff --git a/HalfedgeDS/include/CGAL/HalfedgeDS_list.h b/HalfedgeDS/include/CGAL/HalfedgeDS_list.h
index aecf7b7e29b..664be1c2c30 100644
--- a/HalfedgeDS/include/CGAL/HalfedgeDS_list.h
+++ b/HalfedgeDS/include/CGAL/HalfedgeDS_list.h
@@ -395,7 +395,11 @@ public:
         // halfedges, and f faces. The reservation sizes are a hint for
         // optimizing storage allocation. They are not used here.
 
-    ~HalfedgeDS_list() { clear(); }
+    ~HalfedgeDS_list() noexcept {
+      try {
+        clear();
+      } catch (...) {}
+    }
 
     HalfedgeDS_list( const Self& hds)
     :  vertices( hds.vertices),
diff --git a/Nef_3/include/CGAL/Nef_3/K3_tree.h b/Nef_3/include/CGAL/Nef_3/K3_tree.h
index c3b8aaecffc..b551b5c1625 100644
--- a/Nef_3/include/CGAL/Nef_3/K3_tree.h
+++ b/Nef_3/include/CGAL/Nef_3/K3_tree.h
@@ -442,12 +442,15 @@ friend std::ostream& operator<<
 }
 
 
-~Node() {
+~Node() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+{
   CGAL_NEF_TRACEN("~Node: deleting node...");
-  if( !is_leaf()) {
-    delete left_node;
-    delete right_node;
-  }
+  CGAL_destructor_assertion_catch(
+    if( !is_leaf()) {
+      delete left_node;
+      delete right_node;
+    }
+  );
 }
 
 private:
@@ -1103,9 +1106,12 @@ bool update( Node* node,
   return (left_updated || right_updated);
 }
 
-~K3_tree() {
+~K3_tree() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+{
   CGAL_NEF_TRACEN("~K3_tree: deleting root...");
-  delete root;
+  CGAL_destructor_assertion_catch(
+    delete root;
+  );
 }
 
 private:
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h b/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h
index bc3af7976af..46a6dae4962 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h
@@ -126,7 +126,8 @@ public:
 
   virtual void add_vertex(Vertex_handle) {}
 
-  virtual ~SNC_point_locator() {
+  virtual ~SNC_point_locator() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+  {
     CGAL_NEF_CLOG("");
     CGAL_NEF_CLOG("construction_time:  "<<ct_t.time());
     CGAL_NEF_CLOG("pointlocation_time: "<<pl_t.time());
@@ -422,8 +423,9 @@ public:
     return updated;
   }
 
-  virtual ~SNC_point_locator_by_spatial_subdivision() {
-    CGAL_warning(initialized ||
+  virtual ~SNC_point_locator_by_spatial_subdivision() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+  {
+    CGAL_destructor_warning(initialized ||
                  candidate_provider == 0); // required?
     if(initialized)
       delete candidate_provider;
diff --git a/Nef_S2/include/CGAL/Nef_S2/Sphere_map.h b/Nef_S2/include/CGAL/Nef_S2/Sphere_map.h
index 93670a125e2..0ee5d431292 100644
--- a/Nef_S2/include/CGAL/Nef_S2/Sphere_map.h
+++ b/Nef_S2/include/CGAL/Nef_S2/Sphere_map.h
@@ -229,7 +229,12 @@ public:
   Sphere_map(bool = false) : boundary_item_(boost::none),
     svertices_(), sedges_(), sfaces_(), shalfloop_() {}
 
-  ~Sphere_map() { clear(); }
+  ~Sphere_map() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+  {
+    CGAL_destructor_assertion_catch(
+      clear();
+    );
+  }
 
   Sphere_map(const Self& D) : boundary_item_(boost::none),
     svertices_(D.svertices_),
diff --git a/Nef_S2/include/CGAL/Nef_polyhedron_S2.h b/Nef_S2/include/CGAL/Nef_polyhedron_S2.h
index 10003b5b47a..59613249388 100644
--- a/Nef_S2/include/CGAL/Nef_polyhedron_S2.h
+++ b/Nef_S2/include/CGAL/Nef_polyhedron_S2.h
@@ -73,7 +73,12 @@ class Nef_polyhedron_S2_rep {
 public:
   Nef_polyhedron_S2_rep() : sm_() {}
   Nef_polyhedron_S2_rep(const Self&) : sm_() {}
-  ~Nef_polyhedron_S2_rep() { sm_.clear(); }
+  ~Nef_polyhedron_S2_rep() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+  {
+    CGAL_destructor_assertion_catch(
+      sm_.clear();
+    );
+  }
 };
 
 /*{\Moptions print_title=yes }*/
diff --git a/STL_Extension/include/CGAL/Handle_for.h b/STL_Extension/include/CGAL/Handle_for.h
index 537096b6e73..97543f58db8 100644
--- a/STL_Extension/include/CGAL/Handle_for.h
+++ b/STL_Extension/include/CGAL/Handle_for.h
@@ -149,12 +149,14 @@ public:
         return *this;
     }
 
-    ~Handle_for()
+    ~Handle_for() noexcept
     {
-      if (--(ptr_->count) == 0) {
-        Allocator_traits::destroy(allocator, ptr_);
-        allocator.deallocate( ptr_, 1);
-      }
+      try{
+        if (--(ptr_->count) == 0) {
+          Allocator_traits::destroy(allocator, ptr_);
+          allocator.deallocate( ptr_, 1);
+        }
+      } catch(...) {}
     }
 
     void
diff --git a/STL_Extension/include/CGAL/In_place_list.h b/STL_Extension/include/CGAL/In_place_list.h
index 89fd3da3c82..e19c8ca5e4d 100644
--- a/STL_Extension/include/CGAL/In_place_list.h
+++ b/STL_Extension/include/CGAL/In_place_list.h
@@ -445,9 +445,11 @@ public:
     (*node).prev_link = node;
     insert(begin(), x.begin(), x.end());
   }
-  ~In_place_list() {
-    erase(begin(), end());
-    put_node(node);
+  ~In_place_list() noexcept {
+    try {
+      erase(begin(), end());
+      put_node(node);
+    } catch(...) {}
   }
 
   Self& operator=(const Self& x);
diff --git a/STL_Extension/include/CGAL/assertions.h b/STL_Extension/include/CGAL/assertions.h
index caa0237fc7d..e13f181f970 100644
--- a/STL_Extension/include/CGAL/assertions.h
+++ b/STL_Extension/include/CGAL/assertions.h
@@ -79,6 +79,7 @@ inline bool possibly(Uncertain<bool> c);
 #if defined(CGAL_NO_ASSERTIONS)
 #  define CGAL_assertion(EX) (static_cast<void>(0))
 #  define CGAL_destructor_assertion(EX) (static_cast<void>(0))
+#  define CGAL_destructor_assertion_catch(CODE) CODE
 #  define CGAL_assertion_msg(EX,MSG) (static_cast<void>(0))
 #  define CGAL_assertion_code(CODE)
 #  ifdef CGAL_ASSUME
@@ -94,9 +95,11 @@ inline bool possibly(Uncertain<bool> c);
 #  if __cpp_lib_uncaught_exceptions || ( _MSVC_LANG >= 201703L )  // C++17
 #    define CGAL_destructor_assertion(EX) \
      (CGAL::possibly(EX)||(std::uncaught_exceptions() > 0)?(static_cast<void>(0)): ::CGAL::assertion_fail( # EX , __FILE__, __LINE__))
+#  define CGAL_destructor_assertion_catch(CODE) try{ CODE } catch(...) { if(std::uncaught_exceptions() <= 0) throw; }
 #  else // use C++03 `std::uncaught_exception()`
 #    define CGAL_destructor_assertion(EX) \
      (CGAL::possibly(EX)||std::uncaught_exception()?(static_cast<void>(0)): ::CGAL::assertion_fail( # EX , __FILE__, __LINE__))
+#  define CGAL_destructor_assertion_catch(CODE) try{ CODE } catch(...) { if(!std::uncaught_exception()) throw; }
 #  endif // use C++03 `std::uncaught_exception()`
 #  define CGAL_assertion_msg(EX,MSG)                                    \
    (CGAL::possibly(EX)?(static_cast<void>(0)): ::CGAL::assertion_fail( # EX , __FILE__, __LINE__, MSG))
@@ -293,11 +296,19 @@ inline bool possibly(Uncertain<bool> c);
 
 #if defined(CGAL_NO_WARNINGS)
 #  define CGAL_warning(EX) (static_cast<void>(0))
+#  define CGAL_destructor_warning(EX) (static_cast<void>(0))
 #  define CGAL_warning_msg(EX,MSG) (static_cast<void>(0))
 #  define CGAL_warning_code(CODE)
 #else
 #  define CGAL_warning(EX) \
    (CGAL::possibly(EX)?(static_cast<void>(0)): ::CGAL::warning_fail( # EX , __FILE__, __LINE__))
+#  if __cpp_lib_uncaught_exceptions || ( _MSVC_LANG >= 201703L )  // C++17
+#    define CGAL_destructor_warning(EX) \
+     (CGAL::possibly(EX)||(std::uncaught_exceptions() > 0)?(static_cast<void>(0)): ::CGAL::warning_fail( # EX , __FILE__, __LINE__))
+#  else // use C++03 `std::uncaught_exception()`
+#    define CGAL_destructor_warning(EX) \
+     (CGAL::possibly(EX)||std::uncaught_exception()?(static_cast<void>(0)): ::CGAL::warning_fail( # EX , __FILE__, __LINE__))
+#  endif // use C++03 `std::uncaught_exception()`
 #  define CGAL_warning_msg(EX,MSG) \
    (CGAL::possibly(EX)?(static_cast<void>(0)): ::CGAL::warning_fail( # EX , __FILE__, __LINE__, MSG))
 #  define CGAL_warning_code(CODE) CODE
diff --git a/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_aux.h b/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_aux.h
index 532d72e3a88..7e642e8b10b 100644
--- a/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_aux.h
+++ b/Straight_skeleton_2/include/CGAL/Straight_skeleton_2/Straight_skeleton_aux.h
@@ -164,7 +164,7 @@ private:
   Ref_counted_base& operator=( Ref_counted_base const &);
 protected:
   Ref_counted_base(): mCount(0) {}
-  virtual ~Ref_counted_base() {}
+  virtual ~Ref_counted_base() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL) {}
 public:
     void AddRef() const { ++mCount; }
     void Release() const
diff --git a/Stream_support/include/CGAL/IO/VRML/VRML_2_ostream.h b/Stream_support/include/CGAL/IO/VRML/VRML_2_ostream.h
index 08e8fdd7e49..d200643068d 100644
--- a/Stream_support/include/CGAL/IO/VRML/VRML_2_ostream.h
+++ b/Stream_support/include/CGAL/IO/VRML/VRML_2_ostream.h
@@ -30,7 +30,12 @@ class VRML_2_ostream
 public:
   VRML_2_ostream() : m_os(nullptr) {}
   VRML_2_ostream(std::ostream& o) : m_os(&o) { header(); }
-  ~VRML_2_ostream() { close(); }
+  ~VRML_2_ostream() CGAL_NOEXCEPT(CGAL_NO_ASSERTIONS_BOOL)
+  {
+    CGAL_destructor_assertion_catch(
+      close();
+    );
+  }
 
   void open(std::ostream& o) { m_os = &o; header(); }
   void close()