diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h
index 88231149331..1562582f014 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH2.h
@@ -916,25 +916,26 @@ cartesian(int i, int j) const
             {
               case 0: return FT(_cos) / FT(_den);
               case 1: return - FT(_sin) / FT(_den);
-              case 2: return RT(0);
-              default: CGAL_ASSUME(false);
+              case 2: return FT(0);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
               case 0: return FT(_sin) / FT(_den);
               case 1: return FT(_cos) / FT(_den);
               case 2: return FT(0);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
               case 0: return FT(0);
               case 1: return FT(0);
               case 2: return FT(1);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
-  CGAL_ASSUME(false);
+  CGAL_assume(false);
+  return FT(0);
 }
 
 template < class R >
@@ -950,24 +951,25 @@ homogeneous(int i, int j) const
               case 0: return _sf_num;
               case 1: return RT(0);
               case 2: return RT(0);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
               case 0: return RT(0);
               case 1: return _sf_num;
               case 2: return RT(0);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
               case 0: return RT(0);
               case 1: return RT(0);
               case 2: return _sf_den;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
-  CGAL_ASSUME(false);
+  CGAL_assume(false);
+  return RT(0);
 }
 
 template <class R>
@@ -983,24 +985,25 @@ cartesian(int i, int j) const
               case 0: return FT(_sf_num) / FT(_sf_den);
               case 1: return FT(0);
               case 2: return FT(0);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
               case 0: return FT(0);
               case 1: return FT(_sf_num) / FT(_sf_den);
               case 2: return FT(0);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
               case 0: return FT(0);
               case 1: return FT(0);
               case 2: return FT(1);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
- CGAL_ASSUME(false);
+ CGAL_assume(false);
+ return FT(0);
 }
 
 template < class R >
@@ -1017,24 +1020,25 @@ homogeneous(int i, int j) const
               case 0: return l.b()*l.b() - l.a()*l.a();
               case 1: return l.a()*l.b()*mRT2;
               case 2: return l.a()*l.c()*mRT2;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
               case 0: return l.a()*l.b()*mRT2;
               case 1: return l.a()*l.a() - l.b()*l.b();
               case 2: return l.b()*l.c()*mRT2;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
               case 0: return RT(0);
               case 1: return RT(0);
               case 2: return l.a()*l.a() + l.b()*l.b();
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
-  CGAL_ASSUME(false);
+  CGAL_assume(false);
+  return RT(0);
 }
 
 template <class R>
@@ -1051,24 +1055,25 @@ cartesian(int i, int j) const
               case 0: return FT( l.b()-l.a() ) / FT( l.a()+l.b());
               case 1: return FT( homogeneous(0,1)) / de;
               case 2: return FT( homogeneous(0,2)) / de;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
               case 0: return FT( homogeneous(1,0)) / de;
               case 1: return FT( l.a()-l.b() ) / FT( l.a()+l.b());
               case 2: return FT( homogeneous(1,2)) / de;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
               case 0: return FT(0);
               case 1: return FT(0);
               case 2: return FT(1);
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
-  CGAL_ASSUME(false);
+  CGAL_assume(false);
+  return FT(0);
 }
 
 } //namespace CGAL
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
index 8d05ea24397..8513982844f 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
@@ -551,7 +551,7 @@ homogeneous(int i, int j) const
               case 1: return t01;
               case 2: return t02;
               case 3: return t03;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
@@ -559,7 +559,7 @@ homogeneous(int i, int j) const
               case 1: return t11;
               case 2: return t12;
               case 3: return t13;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
@@ -567,7 +567,7 @@ homogeneous(int i, int j) const
               case 1: return t21;
               case 2: return t22;
               case 3: return t23;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 3: switch (j)
             {
@@ -575,10 +575,11 @@ homogeneous(int i, int j) const
               case 1: return RT0;
               case 2: return RT0;
               case 3: return t33;
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
-  CGAL_ASSUME(false);
+  CGAL_assume(false);
+  return RT0;
 }
 
 template < class R >
@@ -699,7 +700,7 @@ Translation_repH3<R>::homogeneous(int i, int j) const
               case 1: return RT0;
               case 2: return RT0;
               case 3: return tv.hx();
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 1: switch (j)
             {
@@ -707,7 +708,7 @@ Translation_repH3<R>::homogeneous(int i, int j) const
               case 1: return tv.hw();
               case 2: return RT0;
               case 3: return tv.hy();
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 2: switch (j)
             {
@@ -715,7 +716,7 @@ Translation_repH3<R>::homogeneous(int i, int j) const
               case 1: return RT0;
               case 2: return tv.hw();
               case 3: return tv.hz();
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
     case 3: switch (j)
             {
@@ -723,10 +724,11 @@ Translation_repH3<R>::homogeneous(int i, int j) const
               case 1: return RT0;
               case 2: return RT0;
               case 3: return tv.hw();
-              default: CGAL_ASSUME(false);
+              default: CGAL_assume(false);
             }
   }
-  CGAL_ASSUME(false);
+  CGAL_assume(false);
+  return RT0;
 }
 
 template < class R >
diff --git a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
index a6a2dcf60f6..7cb3f9299f2 100644
--- a/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
+++ b/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h
@@ -129,7 +129,7 @@ private:
         return 1;
       case LEFT_TURN:
         return 2;
-      default: CGAL_ASSUME(false);
+      default: CGAL_assume(false);
       }
       return -1;
     }
@@ -223,7 +223,7 @@ private:
                 == Visibility_2::orientation_2(geom_traits, s2, t2, s1);
           else
             return true;
-        default: CGAL_ASSUME(false);
+        default: CGAL_assume(false);
         }
       case LEFT_TURN:
         switch (Visibility_2::orientation_2(geom_traits, s1, t1, s2)) {
@@ -241,7 +241,7 @@ private:
                 == Visibility_2::orientation_2(geom_traits, s2, t2, s1);
           else
             return true;
-        default: CGAL_ASSUME(false);
+        default: CGAL_assume(false);
         }
       }