diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
index 64275864cfe..072eef6ff93 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
@@ -36,12 +36,11 @@
 
 #include <CGAL/Circular_kernel_2/function_objects_polynomial_circular.h>
 #include <CGAL/global_functions_on_circular_arcs_2.h>
+#include <CGAL/global_functions_on_line_arcs_2.h>
 
 #include <CGAL/Circular_kernel_2/function_objects_on_line_2.h>
-#include <CGAL/global_functions_on_line_2.h>
 
 #include <CGAL/Circular_kernel_2/function_objects_on_circle_2.h>
-#include <CGAL/global_functions_on_circle_2.h>
 
 CGAL_BEGIN_NAMESPACE
 
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_point_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_point_2.h
index 707dfec3d46..61606fe77c0 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_point_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2/Circular_arc_point_2.h
@@ -29,7 +29,6 @@
 #include <CGAL/Bbox_2.h>
 #include <CGAL/Interval_nt.h>
 #include <boost/type_traits/is_same.hpp>
-#include <CGAL/global_functions_on_circle_2.h>
 
 namespace CGAL {
 namespace CGALi {
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2/Line_arc_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2/Line_arc_2.h
index 41ff1057d46..ac9de3abc5f 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2/Line_arc_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2/Line_arc_2.h
@@ -25,8 +25,6 @@
 #ifndef CGAL_CIRCULAR_KERNEL_LINE_ARC_2_H
 #define CGAL_CIRCULAR_KERNEL_LINE_ARC_2_H
 
-#include <CGAL/global_functions_on_line_2.h>
-#include <CGAL/global_functions_on_circle_2.h>
 #include <CGAL/global_functions_on_line_arcs_2.h>
 #include <CGAL/intersections.h>
 #include <CGAL/Algebraic_kernel_for_circles/internal_functions_on_roots_and_polynomial_1_2_and_2_2.h>
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_line_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_line_2.h
index c8e2cd4c102..d573eea8958 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_line_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_line_2.h
@@ -83,8 +83,8 @@ namespace LinearFunctors {
     typedef typename CK::Polynomial_for_circles_2_2  Equation_circle; 
     typedef typename CK::Root_for_circles_2_2        Root_for_circles_2_2;
     
-    Equation_line e1 = CGAL::get_equation<CK>(l);
-    Equation_circle e2 = CGAL::get_equation<CK>(c);
+    Equation_line e1 = CK().get_equation_object()(l);
+    Equation_circle e2 = CK().get_equation_object()(c);
     
     typedef std::vector< std::pair < Root_for_circles_2_2, unsigned > > 
       solutions_container;
diff --git a/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
index a07f29315d3..ee9d159d715 100644
--- a/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
@@ -25,20 +25,22 @@
 #ifndef CGAL_SIMPLE_CIRCULAR_KERNEL_2_H
 #define CGAL_SIMPLE_CIRCULAR_KERNEL_2_H
 
-#include <CGAL/Circular_kernel_2/Circular_arc_point_2.h>
-#include <CGAL/Circular_kernel_2/Circular_arc_2.h>
-#include <CGAL/Circular_kernel_2/Line_arc_2.h>
 #include <CGAL/Circular_arc_2.h>
 #include <CGAL/Circular_arc_point_2.h>
 #include <CGAL/Line_arc_2.h>
+#include <CGAL/Circular_kernel_2/Circular_arc_point_2.h>
+#include <CGAL/Circular_kernel_2/Circular_arc_2.h>
+#include <CGAL/Circular_kernel_2/Line_arc_2.h>
 
-#include <CGAL/Circular_kernel_2/function_objects_on_circle_2.h>
-#include <CGAL/global_functions_on_circle_2.h>
+#include <CGAL/Circular_kernel_type_equality_wrapper.h>
 
 #include <CGAL/Circular_kernel_2/function_objects_polynomial_circular.h>
 #include <CGAL/global_functions_on_circular_arcs_2.h>
+#include <CGAL/global_functions_on_line_arcs_2.h>
 
-#include <CGAL/Circular_kernel_type_equality_wrapper.h>
+#include <CGAL/Circular_kernel_2/function_objects_on_line_2.h>
+
+#include <CGAL/Circular_kernel_2/function_objects_on_circle_2.h>
 
 CGAL_BEGIN_NAMESPACE
 
diff --git a/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h b/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h
index 4e76d7ad86c..00908792dc2 100644
--- a/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h
+++ b/Circular_kernel_2/include/CGAL/global_functions_on_circle_2.h
@@ -27,30 +27,6 @@
 
 CGAL_BEGIN_NAMESPACE
 
-template< class CK >
-inline
-typename CK::Polynomial_for_circles_2_2
-get_equation(const Circle_2<CK> & c)
-{
-  return CK().get_equation_object()(c);
-}
-
-template< class CK >
-inline
-Circle_2<CK>
-construct_circle(const typename CK::Polynomial_for_circles_2_2 & eq)
-{
-  return CK().construct_circle_2_object()(eq);
-}
-
-template< class CK >
-inline
-bool
-has_on(const Circle_2<CK> &c, const Circular_arc_point_2<CK> &p)
-{
-  return CK().has_on_2_object()(c, p);
-}
-
 CGAL_END_NAMESPACE
 
 #endif // CGAL_CIRCULAR_KERNEL_GLOBAL_FUNCTIONS_ON_CIRCLE_2_H
diff --git a/Circular_kernel_2/include/CGAL/global_functions_on_circular_arcs_2.h b/Circular_kernel_2/include/CGAL/global_functions_on_circular_arcs_2.h
index f834be23c70..7806037b635 100644
--- a/Circular_kernel_2/include/CGAL/global_functions_on_circular_arcs_2.h
+++ b/Circular_kernel_2/include/CGAL/global_functions_on_circular_arcs_2.h
@@ -156,6 +156,14 @@ make_xy_monotone(const Circular_arc_2<CK> &A, OutputIterator it)
   return CK().make_xy_monotone_2_object()(A, it);
 }
 
+template< class CK >
+inline
+bool
+has_on(const Circle_2<CK> &c, const Circular_arc_point_2<CK> &p)
+{
+  return CK().has_on_2_object()(c, p);
+}
+
 CGAL_END_NAMESPACE
 
 #endif // CGAL_CIRCULAR_KERNEL_GLOBAL_FUNCTIONS_ON_CIRCULAR_ARCS_2_H
diff --git a/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h b/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h
index 126388c5783..b264cbe12c3 100644
--- a/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h
+++ b/Circular_kernel_2/include/CGAL/global_functions_on_line_2.h
@@ -27,21 +27,6 @@
 
 CGAL_BEGIN_NAMESPACE
 
-template< class CK >
-inline
-typename CK::Polynomial_1_2
-get_equation(const Line_2<CK> & l)
-{
-  return CK().get_equation_object()(l);
-}
-
-template< class CK >
-inline
-CGAL::Line_2<CK>
-construct_line(const typename CK::Polynomial_1_2 & eq)
-{
-  return CK().construct_line_2_object()(eq);
-}
 
 CGAL_END_NAMESPACE