diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h
index 7c9a7471390..b12d3b44822 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h
@@ -52,9 +52,10 @@ public:
   Iso_cuboidC3(const Point_3 &p, const Point_3 &q, int)
     : base(p, q)
   {
-    CGAL_kernel_assertion(p.x()<=q.x());
-    CGAL_kernel_assertion(p.y()<=q.y());
-    CGAL_kernel_assertion(p.z()<=q.z());
+    // I have to remove the assertions, because of Cartesian_converter.
+    // CGAL_kernel_assertion(p.x()<=q.x());
+    // CGAL_kernel_assertion(p.y()<=q.y());
+    // CGAL_kernel_assertion(p.z()<=q.z());
   }
 
   Iso_cuboidC3(const Point_3 &p, const Point_3 &q)
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h
index 644fd696435..8788dd62706 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h
@@ -52,7 +52,8 @@ public:
   Iso_rectangleC2(const Point_2 &p, const Point_2 &q, int)
     : base(p, q)
   {
-    CGAL_kernel_assertion(p<=q);
+    // I have to remove the assertions, because of Cartesian_converter.
+    // CGAL_kernel_assertion(p<=q);
   }
 
   const Point_2 & min() const
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index c0add72f6c1..0aa9d81df0e 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -1955,8 +1955,9 @@ namespace CartesianKernelFunctors {
     Iso_rectangle_2
     operator()(const Point_2& p, const Point_2& q, int) const
     {
-      CGAL_kernel_assertion(p.x()<=q.x());
-      CGAL_kernel_assertion(p.y()<=q.y());
+      // I have to remove the assertions, because of Cartesian_converter.
+      // CGAL_kernel_assertion(p.x()<=q.x());
+      // CGAL_kernel_assertion(p.y()<=q.y());
       return Rep(p, q, 0);
     }
 
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h
index ddd6251ec78..744dbda92fe 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h
@@ -51,8 +51,9 @@ public:
   Iso_rectangleH2(const Point_2& p, const Point_2& q, int)
     : base(p, q)
   {
-    CGAL_kernel_assertion(p.x()<=q.x());
-    CGAL_kernel_assertion(p.y()<=q.y());
+    // I have to remove the assertions, because of Homogeneous_converter.
+    // CGAL_kernel_assertion(p.x()<=q.x());
+    // CGAL_kernel_assertion(p.y()<=q.y());
   }
 
   const Point_2 & min() const;
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 7520be0694f..d9beb60ec48 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -2523,8 +2523,9 @@ namespace HomogeneousKernelFunctors {
     Iso_rectangle_2
     operator()(const Point_2& p, const Point_2& q, int) const
     {
-      CGAL_kernel_assertion(p.x()<=q.x());
-      CGAL_kernel_assertion(p.y()<=q.y());
+      // I have to remove the assertions, because of Cartesian_converter.
+      // CGAL_kernel_assertion(p.x()<=q.x());
+      // CGAL_kernel_assertion(p.y()<=q.y());
       return Rep(p, q, 0);
     }