diff --git a/STL_Extension/include/CGAL/Compact_container.h b/STL_Extension/include/CGAL/Compact_container.h
index 86366b6f766..5c4e0b66d59 100644
--- a/STL_Extension/include/CGAL/Compact_container.h
+++ b/STL_Extension/include/CGAL/Compact_container.h
@@ -1077,8 +1077,8 @@ namespace internal {
     {
       CGAL_assertion_msg(m_ptr.p != NULL,
          "Incrementing a singular iterator or an empty container iterator ?");
-      CGAL_assertion_msg(DSC::type(m_ptr.p) == DSC::USED,
-                         "Incrementing an invalid iterator.");
+      /* CGAL_assertion_msg(DSC::type(m_ptr.p) == DSC::USED,
+         "Incrementing an invalid iterator."); */
       increment();
       return *this;
     }
@@ -1087,9 +1087,9 @@ namespace internal {
     {
       CGAL_assertion_msg(m_ptr.p != NULL,
          "Decrementing a singular iterator or an empty container iterator ?");
-      CGAL_assertion_msg(DSC::type(m_ptr.p) == DSC::USED
+      /*CGAL_assertion_msg(DSC::type(m_ptr.p) == DSC::USED
                       || DSC::type(m_ptr.p) == DSC::START_END,
-                         "Decrementing an invalid iterator.");
+                      "Decrementing an invalid iterator.");*/
       decrement();
       return *this;
     }
diff --git a/STL_Extension/include/CGAL/Concurrent_compact_container.h b/STL_Extension/include/CGAL/Concurrent_compact_container.h
index dd06d8c6391..54d15e7885a 100644
--- a/STL_Extension/include/CGAL/Concurrent_compact_container.h
+++ b/STL_Extension/include/CGAL/Concurrent_compact_container.h
@@ -937,8 +937,8 @@ namespace CCC_internal {
     {
       CGAL_assertion_msg(m_ptr.p != NULL,
    "Incrementing a singular iterator or an empty container iterator ?");
-      CGAL_assertion_msg(CCC::type(m_ptr.p) == CCC::USED,
-                         "Incrementing an invalid iterator.");
+      /* CGAL_assertion_msg(CCC::type(m_ptr.p) == CCC::USED,
+         "Incrementing an invalid iterator."); */
       increment();
       return *this;
     }
@@ -947,9 +947,9 @@ namespace CCC_internal {
     {
       CGAL_assertion_msg(m_ptr.p != NULL,
    "Decrementing a singular iterator or an empty container iterator ?");
-      CGAL_assertion_msg(CCC::type(m_ptr.p) == CCC::USED
+      /* CGAL_assertion_msg(CCC::type(m_ptr.p) == CCC::USED
           || CCC::type(m_ptr.p) == CCC::START_END,
-                         "Decrementing an invalid iterator.");
+          "Decrementing an invalid iterator."); */
       decrement();
       return *this;
     }