diff --git a/BGL/include/CGAL/boost/graph/Seam_mesh.h b/BGL/include/CGAL/boost/graph/Seam_mesh.h
index 04352724a0b..ddc3d1971ba 100644
--- a/BGL/include/CGAL/boost/graph/Seam_mesh.h
+++ b/BGL/include/CGAL/boost/graph/Seam_mesh.h
@@ -444,6 +444,7 @@ public:
   {
   public:
     halfedge_descriptor hd;
+    const Self* mesh_;
 
 #ifdef CGAL_SEAM_MESH_INSERT_OPERATOR
     friend
@@ -453,9 +454,24 @@ public:
       return os;
     }
 #endif
-    edge_descriptor(const halfedge_descriptor& hd)
-      : hd(hd)
-    { }
+
+    edge_descriptor()
+      : mesh_(NULL)
+    {}
+
+    edge_descriptor(const halfedge_descriptor& hd, const Self* m)
+      : hd(hd), mesh_(m)
+    {}
+
+    friend bool operator==(edge_descriptor e1, edge_descriptor e2)
+    {
+      return (e1.hd == e2.hd) || (e1.hd == e2.mesh_->opposite(e2.hd)); 
+    }
+
+    friend bool operator!=(edge_descriptor e1, edge_descriptor e2)
+    {
+      return ! (e1 == e2);
+    }
   };
 
 #ifndef DOXYGEN_RUNNING
@@ -534,9 +550,9 @@ public:
       // on the opposite virtual border
 
       if(seam)
-        return edge_descriptor(mesh_->opposite(halfedge_descriptor(*hd, true)));
+        return edge_descriptor(mesh_->opposite(halfedge_descriptor(*hd, true)), mesh_);
       else
-        return edge_descriptor(halfedge_descriptor(*hd, false));
+        return edge_descriptor(halfedge_descriptor(*hd, false), mesh_);
     }
   };
 #endif
@@ -758,7 +774,7 @@ public:
   /// Returns the edge that contains halfedge `h` as one of its two halfedges.
   edge_descriptor edge(halfedge_descriptor h) const
   {
-    return h;
+    return edge_descriptor(h,this);
   }
 
   /// Returns the halfedge corresponding to the edge `e`.
@@ -827,7 +843,7 @@ public:
   std::pair<edge_descriptor, bool> edge(vertex_descriptor u, vertex_descriptor v) const
   {
     std::pair<halfedge_descriptor, bool> he = halfedge(u, v);
-    return std::make_pair(he.first, he.second);
+    return std::make_pair(edge_descriptor(he.first, this), he.second);
   }
 
   /// Returns a halfedge of face `f`.
diff --git a/BGL/include/CGAL/boost/graph/graph_traits_Seam_mesh.h b/BGL/include/CGAL/boost/graph/graph_traits_Seam_mesh.h
index 18a543f72f2..168cfda2d9b 100644
--- a/BGL/include/CGAL/boost/graph/graph_traits_Seam_mesh.h
+++ b/BGL/include/CGAL/boost/graph/graph_traits_Seam_mesh.h
@@ -107,8 +107,8 @@ public:
   typedef typename SM::face_iterator                  face_iterator;
   typedef typename SM::faces_size_type                faces_size_type;
 
-  //typedef CGAL::In_edge_iterator<SM>                  in_edge_iterator;
-  //typedef CGAL::Out_edge_iterator<SM>                 out_edge_iterator;
+  typedef CGAL::In_edge_iterator<SM>                  in_edge_iterator;
+  typedef CGAL::Out_edge_iterator<SM>                 out_edge_iterator;
 
   // nulls
   static vertex_descriptor null_vertex() { return vertex_descriptor(); }
@@ -209,7 +209,7 @@ edges(const CGAL::Seam_mesh<TM, SEM, SVM>& sm)
   return sm.edges();
 }
 
-#if 0
+#if 1
 template <class TM, class SEM, class SVM>
 Iterator_range<typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::in_edge_iterator>
 in_edges(typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::vertex_descriptor v,
@@ -279,7 +279,7 @@ typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::halfedge_descripto
 halfedge(typename boost::graph_traits<CGAL::Seam_mesh<TM, SEM, SVM> >::edge_descriptor e,
          const CGAL::Seam_mesh<TM, SEM, SVM>& sm)
 {
-  return sm.edge(e);
+  return sm.halfedge(e);
 }
 
 template <class TM, class SEM, class SVM>
diff --git a/BGL/test/BGL/CMakeLists.txt b/BGL/test/BGL/CMakeLists.txt
index 4e2bed4842c..9ce23d3de53 100644
--- a/BGL/test/BGL/CMakeLists.txt
+++ b/BGL/test/BGL/CMakeLists.txt
@@ -73,6 +73,8 @@ create_single_source_cgal_program( "graph_concept_Triangulation_2.cpp" )
 
 create_single_source_cgal_program( "graph_concept_Surface_mesh.cpp" )
 
+create_single_source_cgal_program( "graph_concept_Seam_mesh_Surface_mesh.cpp" )
+
 create_single_source_cgal_program( "graph_concept_Gwdwg_Surface_mesh.cpp" )
 
 create_single_source_cgal_program( "test_clear.cpp" )
diff --git a/BGL/test/BGL/graph_concept_Seam_mesh_Surface_mesh.cpp b/BGL/test/BGL/graph_concept_Seam_mesh_Surface_mesh.cpp
new file mode 100644
index 00000000000..75857fc76ae
--- /dev/null
+++ b/BGL/test/BGL/graph_concept_Seam_mesh_Surface_mesh.cpp
@@ -0,0 +1,49 @@
+#include <CGAL/boost/graph/graph_traits_Surface_mesh.h>
+#include <CGAL/boost/graph/properties_Surface_mesh.h>
+#include <CGAL/boost/graph/Seam_mesh.h>
+#include <CGAL/Simple_cartesian.h>
+
+#include <boost/graph/graph_concepts.hpp>
+#include <CGAL/boost/graph/graph_concepts.h>
+
+typedef CGAL::Simple_cartesian<double> K;
+typedef CGAL::Surface_mesh<K::Point_3> Mesh;
+typedef boost::graph_traits<Mesh>::vertex_descriptor         SM_vertex_descriptor;
+typedef boost::graph_traits<Mesh>::halfedge_descriptor       SM_halfedge_descriptor;
+typedef boost::graph_traits<Mesh>::edge_descriptor           SM_edge_descriptor;
+typedef boost::graph_traits<Mesh>::face_descriptor           SM_face_descriptor;
+
+typedef Mesh::Property_map<SM_edge_descriptor, bool>            Seam_edge_pmap;
+typedef Mesh::Property_map<SM_vertex_descriptor, bool>          Seam_vertex_pmap;
+typedef CGAL::Seam_mesh<Mesh, Seam_edge_pmap, Seam_vertex_pmap> Seam_mesh;
+
+typedef boost::graph_traits< Seam_mesh > Traits;
+typedef Traits::edge_descriptor edge_descriptor;
+typedef Traits::halfedge_descriptor halfedge_descriptor;
+typedef Traits::vertex_descriptor vertex_descriptor;
+typedef Traits::face_descriptor face_descriptor;
+
+void concept_check_surface_mesh()
+{
+  boost::function_requires< boost::GraphConcept<Seam_mesh> >();
+  boost::function_requires< boost::VertexListGraphConcept<Seam_mesh> >();
+  boost::function_requires< boost::EdgeListGraphConcept<Seam_mesh> >();
+  boost::function_requires< boost::IncidenceGraphConcept<Seam_mesh> >();
+  boost::function_requires< boost::AdjacencyMatrixConcept<Seam_mesh> >();
+  boost::function_requires< boost::BidirectionalGraphConcept<Seam_mesh> >();
+  boost::function_requires< CGAL::HalfedgeGraphConcept<Seam_mesh> >();
+  boost::function_requires< CGAL::HalfedgeListGraphConcept<Seam_mesh> >();
+  boost::function_requires< CGAL::FaceGraphConcept<Seam_mesh> >();
+  boost::function_requires< CGAL::FaceListGraphConcept<Seam_mesh> >();
+
+
+  // null
+  boost::graph_traits<Seam_mesh>::null_vertex();
+  boost::graph_traits<Seam_mesh>::null_face();
+}
+
+int main()
+{
+  concept_check_surface_mesh();
+  return 0;
+}