diff --git a/Number_types/include/CGAL/FPU.h b/Number_types/include/CGAL/FPU.h
index 241a129ec78..46e00349ee7 100644
--- a/Number_types/include/CGAL/FPU.h
+++ b/Number_types/include/CGAL/FPU.h
@@ -140,8 +140,9 @@ inline double IA_force_to_double(double x)
 // which has the same problem.  This affects underflow and overflow cases.
 // In case one does not care about such "extreme" situations, one can
 // set CGAL_IA_NO_X86_OVER_UNDER_FLOW_PROTECT.
-#if defined CGAL_FPU_HAS_EXCESS_PRECISION && \
-   !defined CGAL_IA_NO_X86_OVER_UNDER_FLOW_PROTECT
+// LLVM doesn't have -frounding-math so needs extra protection.
+#if (defined CGAL_FPU_HAS_EXCESS_PRECISION && \
+   !defined CGAL_IA_NO_X86_OVER_UNDER_FLOW_PROTECT) || defined __llvm__
 #  define CGAL_IA_FORCE_TO_DOUBLE(x) CGAL::IA_force_to_double(x)
 #else
 #  define CGAL_IA_FORCE_TO_DOUBLE(x) (x)
diff --git a/STL_Extension/src/CGAL/assertions.cpp b/STL_Extension/src/CGAL/assertions.cpp
index 095e311a5e0..420e9c5fb66 100644
--- a/STL_Extension/src/CGAL/assertions.cpp
+++ b/STL_Extension/src/CGAL/assertions.cpp
@@ -49,7 +49,7 @@ _standard_error_handler(
         int         line,
         const char* msg )
 {
-#if defined(__GNUG__) && !defined(__clang__)
+#if defined(__GNUG__) && !defined(__llvm__)
     // After g++ 3.4, std::terminate defaults to printing to std::cerr itself.
     if (_error_behaviour == THROW_EXCEPTION)
         return;
@@ -73,7 +73,7 @@ _standard_warning_handler( const char *,
                           int         line,
                           const char* msg )
 {
-#if defined(__GNUG__) && !defined(__clang__)
+#if defined(__GNUG__) && !defined(__llvm__)
     // After g++ 3.4, std::terminate defaults to printing to std::cerr itself.
     if (_warning_behaviour == THROW_EXCEPTION)
         return;