diff --git a/Mesh_3/include/CGAL/Mesh_3/Refine_cells_3.h b/Mesh_3/include/CGAL/Mesh_3/Refine_cells_3.h
index 654dd4bc951..970ce666753 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Refine_cells_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Refine_cells_3.h
@@ -394,7 +394,7 @@ public:
   }
 
   // Tells if the refinement process of cells is currently finished
-  bool no_longer_element_to_refine_impl() const
+  bool no_longer_element_to_refine_impl()
   {
     if(m_maximal_number_of_vertices_ !=0 &&
        triangulation_ref_impl().number_of_vertices() >=
diff --git a/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h b/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h
index 8347a1fe040..8bd49342a3f 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Refine_facets_3.h
@@ -294,7 +294,7 @@ public:
   void scan_triangulation_impl_amendement() const {}
 
   // Tells if the refinement process of cells is currently finished
-  bool no_longer_element_to_refine_impl() const
+  bool no_longer_element_to_refine_impl()
   {
     if(m_maximal_number_of_vertices_ !=0 &&
        r_tr_.number_of_vertices() >=