diff --git a/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_circulator.h b/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_circulator.h
index 3b9e70873cb..cfe7e8cbaa8 100644
--- a/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_circulator.h
+++ b/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_circulator.h
@@ -31,13 +31,6 @@
 
 CGAL_BEGIN_NAMESPACE
 
-//-----------------------------------------------------------------------//
-//                          Polygon_2_const_edge_circulator
-//-----------------------------------------------------------------------//
-// Ideally the class Polygon_2_const_edge_circulator would be a nested
-// class of Polygon_2, but this leads to compiler problems with
-// SGI C++ 4.0 with the iterator_category() function
-
 template <class _Traits, class _Container> class Polygon_2;
 
 template <class _Traits, class _Container>
@@ -136,7 +129,7 @@ class Polygon_2_const_edge_circulator {
     }
 
     Polygon_2_const_edge_circulator<_Traits, _Container>
-    operator+(difference_type n)
+    operator+(difference_type n) const
     {
       return Polygon_2_const_edge_circulator<_Traits, _Container>(
         this->container, first_vertex + n);
@@ -149,7 +142,7 @@ class Polygon_2_const_edge_circulator {
     }
 
     Polygon_2_const_edge_circulator<_Traits, _Container>
-    operator-(difference_type n)
+    operator-(difference_type n) const
     {
       return Polygon_2_const_edge_circulator<_Traits, _Container>(
         this->container, first_vertex - n);
@@ -157,37 +150,37 @@ class Polygon_2_const_edge_circulator {
 
     difference_type
     operator-(
-      const Polygon_2_const_edge_circulator<_Traits, _Container>& a)
+      const Polygon_2_const_edge_circulator<_Traits, _Container>& a) const
     {
       return first_vertex - a.first_vertex;
     }
 
-    Segment_2 operator[](int n)
+    Segment_2 operator[](int n) const
     {
       return *Polygon_2_const_edge_circulator<_Traits, _Container>(
         this->container, first_vertex+n);
     }
 
     bool operator<(
-      const Polygon_2_const_edge_circulator<_Traits, _Container>& a)
+      const Polygon_2_const_edge_circulator<_Traits, _Container>& a) const
     {
       return first_vertex < a.first_vertex;
     }
 
     bool operator>(
-      const Polygon_2_const_edge_circulator<_Traits, _Container>& a)
+      const Polygon_2_const_edge_circulator<_Traits, _Container>& a) const
     {
       return first_vertex > a.first_vertex;
     }
 
     bool operator<=(
-      const Polygon_2_const_edge_circulator<_Traits, _Container>& a)
+      const Polygon_2_const_edge_circulator<_Traits, _Container>& a) const
     {
       return first_vertex <= a.first_vertex;
     }
 
     bool operator>=(
-      const Polygon_2_const_edge_circulator<_Traits, _Container>& a)
+      const Polygon_2_const_edge_circulator<_Traits, _Container>& a) const
     {
       return first_vertex >= a.first_vertex;
     }
@@ -229,4 +222,3 @@ value_type(const Polygon_2_const_edge_circulator<_Traits,_Container>&)
 CGAL_END_NAMESPACE
 
 #endif
-
diff --git a/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_iterator.h b/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_iterator.h
index 69d7c91c43f..a600409e8d4 100644
--- a/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_iterator.h
+++ b/Polygon/include/CGAL/Polygon_2/Polygon_2_edge_iterator.h
@@ -29,13 +29,6 @@
 
 CGAL_BEGIN_NAMESPACE
 
-//-----------------------------------------------------------------------//
-//                          Polygon_2_edge_iterator
-//-----------------------------------------------------------------------//
-// Ideally the class Polygon_2_edge_iterator would be a nested class of
-// Polygon_2, but this leads to compiler problems with SGI C++ 4.0
-// with the iterator_category() function
-
 template <class Traits_, class Container_> class Polygon_2;
 
 template <class Segment_>
@@ -80,7 +73,7 @@ class Polygon_2_edge_iterator {
       return !(first_vertex == x.first_vertex);
     }
 
-    Segment_2 operator*() {
+    Segment_2 operator*() const {
       const_iterator second_vertex = first_vertex;
       ++second_vertex;
       if (second_vertex == container->end())
@@ -90,7 +83,7 @@ class Polygon_2_edge_iterator {
       return construct_segment_2(*first_vertex, *second_vertex);
     }
     
-    Polygon_2__Segment_ptr<Segment_2> operator->()
+    Polygon_2__Segment_ptr<Segment_2> operator->() const
         {return Polygon_2__Segment_ptr<Segment_2>(operator*());}
 
     Polygon_2_edge_iterator<Traits_, Container_>& operator++() {
@@ -123,7 +116,7 @@ class Polygon_2_edge_iterator {
     }
 
     Polygon_2_edge_iterator<Traits_, Container_>
-    operator+(difference_type n) {
+    operator+(difference_type n) const {
       return Polygon_2_edge_iterator<Traits_, Container_>(
         container, first_vertex + n);
     }
@@ -134,37 +127,37 @@ class Polygon_2_edge_iterator {
     }
 
     Polygon_2_edge_iterator<Traits_, Container_>
-    operator-(difference_type n) {
+    operator-(difference_type n) const {
       return Polygon_2_edge_iterator<Traits_, Container_>(
         container, first_vertex - n);
     }
 
     difference_type
-    operator-(const Polygon_2_edge_iterator<Traits_, Container_>& a) {
+    operator-(const Polygon_2_edge_iterator<Traits_, Container_>& a) const {
       return first_vertex - a.first_vertex;
     }
 
-    Segment_2 operator[](int n) {
+    Segment_2 operator[](int n) const {
       return *Polygon_2_edge_iterator<Traits_, Container_>(
         container, first_vertex+n);
     }
 
-    bool operator<(const Polygon_2_edge_iterator<Traits_, Container_>& a)
+    bool operator<(const Polygon_2_edge_iterator<Traits_, Container_>& a) const
     {
       return first_vertex < a.first_vertex;
     }
 
-    bool operator>(const Polygon_2_edge_iterator<Traits_, Container_>& a)
+    bool operator>(const Polygon_2_edge_iterator<Traits_, Container_>& a) const
     {
       return first_vertex > a.first_vertex;
     }
 
-    bool operator<=(const Polygon_2_edge_iterator<Traits_, Container_>& a)
+    bool operator<=(const Polygon_2_edge_iterator<Traits_, Container_>& a) const
     {
       return first_vertex <= a.first_vertex;
     }
 
-    bool operator>=(const Polygon_2_edge_iterator<Traits_, Container_>& a)
+    bool operator>=(const Polygon_2_edge_iterator<Traits_, Container_>& a) const
     {
       return first_vertex >= a.first_vertex;
     }
@@ -201,4 +194,3 @@ value_type(const Polygon_2_edge_iterator<Traits_,Container_>&)
 CGAL_END_NAMESPACE
 
 #endif
-