diff --git a/Lib/test/test_list.py b/Lib/test/test_list.py
index fe4b2cd..b10a833 100644
--- a/Lib/test/test_list.py
+++ b/Lib/test/test_list.py
@@ -171,5 +171,31 @@
         self.assertEqual(iter_size, sys.getsizeof(list([0] * 10)))
         self.assertEqual(iter_size, sys.getsizeof(list(range(10))))
 
+    def test_count_index_remove_crashes(self):
+        # bpo-38610: The count(), index(), and remove() methods were not
+        # holding strong references to list elements while calling
+        # PyObject_RichCompareBool().
+        class X:
+            def __eq__(self, other):
+                lst.clear()
+                return NotImplemented
+
+        lst = [X()]
+        with self.assertRaises(ValueError):
+            lst.index(lst)
+
+        class L(list):
+            def __eq__(self, other):
+                str(other)
+                return NotImplemented
+
+        lst = L([X()])
+        lst.count(lst)
+
+        lst = L([X()])
+        with self.assertRaises(ValueError):
+            lst.remove(lst)
+
+
 if __name__ == "__main__":
     unittest.main()
diff --git a/Misc/NEWS.d/next/Core and Builtins/2019-10-31-14-30-39.bpo-38610.fHdVMS.rst b/Misc/NEWS.d/next/Core and Builtins/2019-10-31-14-30-39.bpo-38610.fHdVMS.rst
new file mode 100644
index 0000000..0ee63bb
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2019-10-31-14-30-39.bpo-38610.fHdVMS.rst
@@ -0,0 +1,2 @@
+Fix possible crashes in several list methods by holding strong references to
+list elements when calling :c:func:`PyObject_RichCompareBool`.
diff --git a/Objects/listobject.c b/Objects/listobject.c
index 645742b..86690f7 100644
--- a/Objects/listobject.c
+++ b/Objects/listobject.c
@@ -2553,7 +2553,10 @@
             stop = 0;
     }
     for (i = start; i < stop && i < Py_SIZE(self); i++) {
-        int cmp = PyObject_RichCompareBool(self->ob_item[i], value, Py_EQ);
+        PyObject *obj = self->ob_item[i];
+        Py_INCREF(obj);
+        int cmp = PyObject_RichCompareBool(obj, value, Py_EQ);
+        Py_DECREF(obj);
         if (cmp > 0)
             return PyLong_FromSsize_t(i);
         else if (cmp < 0)
@@ -2580,7 +2583,10 @@
     Py_ssize_t i;
 
     for (i = 0; i < Py_SIZE(self); i++) {
-        int cmp = PyObject_RichCompareBool(self->ob_item[i], value, Py_EQ);
+        PyObject *obj = self->ob_item[i];
+        Py_INCREF(obj);
+        int cmp = PyObject_RichCompareBool(obj, value, Py_EQ);
+        Py_DECREF(obj);
         if (cmp > 0)
             count++;
         else if (cmp < 0)
@@ -2607,7 +2613,10 @@
     Py_ssize_t i;
 
     for (i = 0; i < Py_SIZE(self); i++) {
-        int cmp = PyObject_RichCompareBool(self->ob_item[i], value, Py_EQ);
+        PyObject *obj = self->ob_item[i];
+        Py_INCREF(obj);
+        int cmp = PyObject_RichCompareBool(obj, value, Py_EQ);
+        Py_DECREF(obj);
         if (cmp > 0) {
             if (list_ass_slice(self, i, i+1,
                                (PyObject *)NULL) == 0)