diff --git a/src/_time_machine.c b/src/_time_machine.c
index e45c675b..211f8a42 100644
--- a/src/_time_machine.c
+++ b/src/_time_machine.c
@@ -511,6 +511,14 @@ _time_machine_patch(PyObject *module, PyObject *unused)
         Py_RETURN_NONE;
 
     PyObject *datetime_module = PyImport_ImportModule("datetime");
+    if (datetime_module == NULL) {
+        return NULL;  // Propagate ImportError
+    }
+    PyObject *time_module = PyImport_ImportModule("time");
+    if (time_module == NULL) {
+        Py_DECREF(datetime_module);
+        return NULL;  // Propagate ImportError
+    }
     PyObject *datetime_class = PyObject_GetAttrString(datetime_module, "datetime");
 
     PyCFunctionObject *datetime_datetime_now =
@@ -532,8 +540,6 @@ _time_machine_patch(PyObject *module, PyObject *unused)
     Py_DECREF(datetime_class);
     Py_DECREF(datetime_module);
 
-    PyObject *time_module = PyImport_ImportModule("time");
-
     /*
         time.clock_gettime(), only available on Unix platforms.
     */
@@ -625,6 +631,14 @@ _time_machine_unpatch(PyObject *module, PyObject *unused)
         Py_RETURN_NONE;
 
     PyObject *datetime_module = PyImport_ImportModule("datetime");
+    if (datetime_module == NULL) {
+        return NULL;  // Propagate ImportError
+    }
+    PyObject *time_module = PyImport_ImportModule("time");
+    if (time_module == NULL) {
+        Py_DECREF(datetime_module);
+        return NULL;  // Propagate ImportError
+    }
     PyObject *datetime_class = PyObject_GetAttrString(datetime_module, "datetime");
 
     PyCFunctionObject *datetime_datetime_now =
@@ -646,8 +660,6 @@ _time_machine_unpatch(PyObject *module, PyObject *unused)
     Py_DECREF(datetime_class);
     Py_DECREF(datetime_module);
 
-    PyObject *time_module = PyImport_ImportModule("time");
-
     /*
         time.clock_gettime(), only available on Unix platforms.
     */
diff --git a/tests/test_time_machine.py b/tests/test_time_machine.py
index c58f770f..14eb7fd9 100644
--- a/tests/test_time_machine.py
+++ b/tests/test_time_machine.py
@@ -827,6 +827,42 @@ def test_uuid1():
 # error handling tests
 
 
+@pytest.mark.parametrize(
+    "module",
+    [
+        "datetime",
+        "time",
+    ],
+)
+def test_start_import_error(module):
+    with (
+        mock.patch.dict(sys.modules, {module: None}),
+        pytest.raises(ModuleNotFoundError) as excinfo,
+    ):
+        time_machine.travel(EPOCH).start()
+
+    assert excinfo.value.args == (f"import of {module} halted; None in sys.modules",)
+
+
+@pytest.mark.parametrize(
+    "module",
+    [
+        "datetime",
+        "time",
+    ],
+)
+def test_stop_import_error(module):
+    traveller = time_machine.travel(EPOCH)
+    traveller.start()
+    with (
+        mock.patch.dict(sys.modules, {module: None}),
+        pytest.raises(ModuleNotFoundError) as excinfo,
+    ):
+        traveller.stop()
+
+    assert excinfo.value.args == (f"import of {module} halted; None in sys.modules",)
+
+
 @pytest.mark.parametrize(
     "func, args",
     [