diff --git a/Lib/test/test_capi/test_long.py b/Lib/test/test_capi/test_long.py
index d45ac75c822ea9..a371f634432b6d 100644
--- a/Lib/test/test_capi/test_long.py
+++ b/Lib/test/test_capi/test_long.py
@@ -211,9 +211,8 @@ def check_long_asintandoverflow(self, func, min_val, max_val):
 
         self.assertEqual(func(min_val - 1), (-1, -1))
         self.assertEqual(func(max_val + 1), (-1, +1))
-
-        # CRASHES func(1.0)
-        # CRASHES func(NULL)
+        self.assertRaises(SystemError, func, None)
+        self.assertRaises(TypeError, func, 1.0)
 
     def test_long_asint(self):
         # Test PyLong_AsInt()
diff --git a/Modules/_testlimitedcapi/long.c b/Modules/_testlimitedcapi/long.c
index b9c35803b423c2..d896435c99a169 100644
--- a/Modules/_testlimitedcapi/long.c
+++ b/Modules/_testlimitedcapi/long.c
@@ -625,7 +625,8 @@ pylong_aslongandoverflow(PyObject *module, PyObject *arg)
     int overflow = UNINITIALIZED_INT;
     long value = PyLong_AsLongAndOverflow(arg, &overflow);
     if (value == -1 && PyErr_Occurred()) {
-        assert(overflow == -1);
+        // overflow can be 0 if a separate exception occurred
+        assert(overflow == -1 || overflow == 0);
         return NULL;
     }
     return Py_BuildValue("li", value, overflow);
@@ -671,7 +672,8 @@ pylong_aslonglongandoverflow(PyObject *module, PyObject *arg)
     int overflow = UNINITIALIZED_INT;
     long long value = PyLong_AsLongLongAndOverflow(arg, &overflow);
     if (value == -1 && PyErr_Occurred()) {
-        assert(overflow == -1);
+        // overflow can be 0 if a separate exception occurred
+        assert(overflow == -1 || overflow == 0);
         return NULL;
     }
     return Py_BuildValue("Li", value, overflow);