diff --git a/Cartesian_kernel/include/CGAL/Cartesian_converter.h b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
index d77689adca9..fb25953c85f 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian_converter.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
@@ -32,6 +32,7 @@
 // provided you give a NT converter from A to B.
 // There's a Homogeneous counterpart.
 
+#include <CGAL/Cartesian_converter_fwd.h>
 #include <CGAL/basic.h>
 #include <CGAL/NT_converter.h>
 #include <CGAL/Enum_converter.h>
@@ -91,7 +92,7 @@ struct Converting_visitor : boost::static_visitor<> {
 
 template < class K1, class K2,
 //          class Converter = NT_converter<typename K1::FT, typename K2::FT> >
-           class Converter = typename internal::Default_converter<K1, K2>::Type >
+           class Converter>
 class Cartesian_converter : public Enum_converter
 {
     typedef Enum_converter   Base;
diff --git a/Installation/CHANGES.md b/Installation/CHANGES.md
index aaca52d651b..82f399e9dba 100644
--- a/Installation/CHANGES.md
+++ b/Installation/CHANGES.md
@@ -18,6 +18,11 @@ Release date: September 2018
     ConstructProjectedPoint 3.
 
 
+### CGAL and Boost Property Maps
+
+-   Addition of a read-write property map to convert on-the-fly geometric 
+    object from Cartesian kernels
+
 ### 2D Triangulations
 
 -   Added a new type of intersection to deal with insertion of a constraints 
diff --git a/Installation/include/CGAL/Cartesian_converter_fwd.h b/Installation/include/CGAL/Cartesian_converter_fwd.h
new file mode 100644
index 00000000000..2e265bc205c
--- /dev/null
+++ b/Installation/include/CGAL/Cartesian_converter_fwd.h
@@ -0,0 +1,42 @@
+// Copyright (C) 2018  GeometryFactory Sarl
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0+
+//
+
+#ifndef CGAL_CARTESIAN_CONVERTER_FWD_H
+#define CGAL_CARTESIAN_CONVERTER_FWD_H
+
+/// \file Cartesian_converter_fwd.h
+/// Forward declarations of the `Cartesian_converter` class.
+
+#ifndef DOXYGEN_RUNNING
+namespace CGAL {
+
+namespace internal {
+template < typename K1, typename K2 >
+struct Default_converter;
+}//internal
+
+template < class K1, class K2,
+           class Converter = typename internal::Default_converter<K1, K2>::Type >
+class Cartesian_converter;
+
+} // CGAL
+#endif
+
+#endif /* CGAL_CARTESIAN_CONVERTER_FWD_H */
+
+
diff --git a/Installation/include/CGAL/Kernel_traits_fwd.h b/Installation/include/CGAL/Kernel_traits_fwd.h
new file mode 100644
index 00000000000..0f7359e7b72
--- /dev/null
+++ b/Installation/include/CGAL/Kernel_traits_fwd.h
@@ -0,0 +1,33 @@
+// Copyright (C) 2018  GeometryFactory Sarl
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: LGPL-3.0+
+//
+
+#ifndef CGAL_KERNEL_TRAITS_FWD_H
+#define CGAL_KERNEL_TRAITS_FWD_H
+
+/// \file Kernel_traits_fwd.h
+/// Forward declarations of the `Kernel_traits` class.
+
+#ifndef DOXYGEN_RUNNING
+namespace CGAL {
+
+template <class T> struct Kernel_traits;
+
+} // CGAL
+#endif
+
+#endif // CGAL_KERNEL_TRAITS_FWD_H
diff --git a/Kernel_23/include/CGAL/Kernel_traits.h b/Kernel_23/include/CGAL/Kernel_traits.h
index e52020fcb47..dc5d38257c0 100644
--- a/Kernel_23/include/CGAL/Kernel_traits.h
+++ b/Kernel_23/include/CGAL/Kernel_traits.h
@@ -26,6 +26,7 @@
 #ifndef CGAL_KERNEL_TRAITS_H
 #define CGAL_KERNEL_TRAITS_H
 
+#include <CGAL/Kernel_traits_fwd.h>
 #include <boost/mpl/has_xxx.hpp>
 #include <boost/mpl/if.hpp>
 
diff --git a/Property_map/include/CGAL/property_map.h b/Property_map/include/CGAL/property_map.h
index a4f5c52d3fd..d025f3962e2 100644
--- a/Property_map/include/CGAL/property_map.h
+++ b/Property_map/include/CGAL/property_map.h
@@ -36,6 +36,9 @@
 
 #include <utility> // defines std::pair
 
+#include <CGAL/Cartesian_converter_fwd.h>
+#include <CGAL/Kernel_traits_fwd.h>
+
 namespace CGAL {
 
 /// \cond SKIP_DOXYGEN
@@ -469,7 +472,7 @@ struct Constant_property_map
 };
 
 /// \ingroup PkgProperty_map
-/// Read-write Property map turning a set (such a `std::set`,
+/// Read-write property map turning a set (such a `std::set`,
 /// `boost::unordered_set`, `std::unordered_set`) into a property map
 /// associating a Boolean to the value type of the set. The function `get` will
 /// return `true` if the key is inside the set and `false` otherwise. The `put`
@@ -515,6 +518,50 @@ make_boolean_property_map(Set& set_)
   return Boolean_property_map<Set>(set_);
 }
 
+/// \ingroup PkgProperty_map
+/// Read-write property map doing on-the-fly conversions between two default constructible \cgal %Cartesian kernels.
+/// Its value type is `GeomObject` and its key type is the same as `Vpm`.
+/// `GeomObject` must be a geometric object from a \cgal kernel.
+/// `Vpm` is a model `of ReadWritePropertyMap` and its value type must be
+/// a geometric object of the same type as `GeomObject` but possibly from
+/// another kernel.
+/// Conversions between the two geometric objects are done using `Cartesian_converter`.
+/// \cgalModels `ReadWritePropertyMap`
+template<class GeomObject, class Vpm>
+struct Cartesian_converter_property_map
+{
+  typedef typename boost::property_traits<Vpm>::key_type key_type;
+  typedef GeomObject value_type;
+  typedef value_type reference;
+  typedef boost::read_write_property_map_tag category;
+  Vpm vpm;
+
+  typedef typename Kernel_traits<GeomObject>::type K2;
+  typedef typename Kernel_traits<typename boost::property_traits<Vpm>::value_type>::type K1;
+
+  Cartesian_converter_property_map(Vpm vpm):vpm(vpm){}
+
+  friend value_type get(const Cartesian_converter_property_map<GeomObject, Vpm>& pm, const key_type& k)
+  {
+    return
+     CGAL::Cartesian_converter<K1, K2>()(get(pm.vpm, k));
+  }
+
+  friend void put(Cartesian_converter_property_map<GeomObject, Vpm>& pm, const key_type& k, const value_type& v)
+  {
+    put(pm.vpm, k, CGAL::Cartesian_converter<K2, K1>()(v));
+  }
+};
+
+/// \ingroup PkgProperty_map
+/// returns `Cartesian_converter_property_map<GeomObject, Vpm>(vpm)`
+template<class GeomObject, class Vpm>
+Cartesian_converter_property_map<GeomObject, Vpm>
+make_cartesian_converter_property_map(Vpm vpm)
+{
+  return Cartesian_converter_property_map<GeomObject, Vpm>(vpm);
+}
+
 } // namespace CGAL
 
 
diff --git a/Property_map/test/Property_map/CMakeLists.txt b/Property_map/test/Property_map/CMakeLists.txt
index 768e08015fb..cf2d22c7469 100644
--- a/Property_map/test/Property_map/CMakeLists.txt
+++ b/Property_map/test/Property_map/CMakeLists.txt
@@ -55,6 +55,8 @@ create_single_source_cgal_program( "dynamic_property_map.cpp" )
 
 create_single_source_cgal_program( "dynamic_properties_test.cpp" )
 
+create_single_source_cgal_program( "kernel_converter_properties_test.cpp" )
+
 if(OpenMesh_FOUND)
         target_link_libraries( dynamic_properties_test PRIVATE ${OPENMESH_LIBRARIES} )
 endif()
diff --git a/Property_map/test/Property_map/kernel_converter_properties_test.cpp b/Property_map/test/Property_map/kernel_converter_properties_test.cpp
new file mode 100644
index 00000000000..586cdd49383
--- /dev/null
+++ b/Property_map/test/Property_map/kernel_converter_properties_test.cpp
@@ -0,0 +1,37 @@
+
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Surface_mesh.h>
+#include <CGAL/Quotient.h>
+#include <CGAL/MP_Float.h>
+#include <CGAL/Cartesian_converter.h>
+#include <CGAL/property_map.h>
+
+typedef CGAL::Simple_cartesian<double> K1;
+typedef CGAL::Simple_cartesian<CGAL::Quotient<CGAL::MP_Float> >  K2;
+typedef K1::Point_3 Point_3;
+
+template <typename Mesh>
+void
+test()
+{
+  Mesh m;
+  CGAL::make_triangle(Point_3(2,0,0),Point_3(1,0,0),Point_3(1,1,0),m);
+
+  typedef typename boost::property_map<Mesh, CGAL::vertex_point_t >::type VPMap;
+  VPMap vmap = get(CGAL::vertex_point, m);
+  
+  CGAL::Cartesian_converter_property_map<K2::Point_3, VPMap> kcmap =CGAL::make_cartesian_converter_property_map<K2::Point_3>(vmap);
+  CGAL_assertion(get(kcmap, *vertices(m).begin()) == CGAL::Point_3<K2>(2,0,0));
+  put(kcmap, *vertices(m).begin(), CGAL::Point_3<K2>(0,2,3));
+  CGAL_assertion(get(kcmap, *vertices(m).begin()) == CGAL::Point_3<K2>(0,2,3));
+  
+}
+  
+int main()
+{
+  
+  typedef CGAL::Surface_mesh<Point_3> SM;
+  test<SM>();
+  return 0;
+}
+