diff --git a/Tests/RunCMake/CMakeLists.txt b/Tests/RunCMake/CMakeLists.txt
index c92aac1484..e8fc9dad84 100644
--- a/Tests/RunCMake/CMakeLists.txt
+++ b/Tests/RunCMake/CMakeLists.txt
@@ -747,6 +747,7 @@ add_RunCMake_test(set_property)
 add_RunCMake_test(string
   -DCMAKE_SYSTEM_NAME=${CMAKE_SYSTEM_NAME}
   -DCMAKE_SYSTEM_PROCESSOR=${CMAKE_SYSTEM_PROCESSOR}
+  -DCMake_TEST_NO_64BIT_TIME=${CMake_TEST_NO_64BIT_TIME}
   )
 add_RunCMake_test(test_include_dirs)
 add_RunCMake_test(BundleUtilities)
diff --git a/Tests/RunCMake/string/RunCMakeTest.cmake b/Tests/RunCMake/string/RunCMakeTest.cmake
index 6baf6214fc..b0aabb6ca2 100644
--- a/Tests/RunCMake/string/RunCMakeTest.cmake
+++ b/Tests/RunCMake/string/RunCMakeTest.cmake
@@ -23,6 +23,7 @@ run_cmake(JoinNoVar)
 run_cmake(Timestamp)
 if(NOT CMAKE_SYSTEM_NAME STREQUAL "AIX" # FIXME: Needs 64-bit build
     AND NOT CMAKE_SYSTEM_NAME STREQUAL "SunOS" # FIXME: Needs 64-bit build
+    AND NOT CMake_TEST_NO_64BIT_TIME
     )
   run_cmake(Timestamp2038)
 endif()