@@ -426,6 +426,13 @@ def permutations2(iterable, r=None):
                 for proto in range(pickle.HIGHEST_PROTOCOL + 1):
                     self.pickletest(proto, permutations(values, r))     # test pickling
 
+    @support.bigaddrspacetest
+    def test_permutations_overflow(self):
+        with self.assertRaises(OverflowError):
+            permutations("A", 2**30)
+        with self.assertRaises(OverflowError):
+            permutations("A", 2, 2**30)
+
     @support.impl_detail("tuple reuse is specific to CPython")
     def test_permutations_tuple_reuse(self):
         self.assertEqual(len(set(map(id, permutations('abcde', 3)))), 1)
@@ -955,6 +962,11 @@ def product2(*args, **kwds):
             args = map(iter, args)
             self.assertEqual(len(list(product(*args))), expected_len)
 
+    @support.bigaddrspacetest
+    def test_product_overflow(self):
+        with self.assertRaises(OverflowError):
+            product(["a"]*(2**16), repeat=2**16)
+
     @support.impl_detail("tuple reuse is specific to CPython")
     def test_product_tuple_reuse(self):
         self.assertEqual(len(set(map(id, product('abc', 'def')))), 1)
 
@@ -50,6 +50,10 @@ Core and Builtins
 Library
 -------
 
+- Issue #23363: Fix possible overflow in itertools.permutations.
+
+- Issue #23364: Fix possible overflow in itertools.product.
+
 - Issue #23366: Fixed possible integer overflow in itertools.combinations.
 
 - Issue #23366: Fixed possible integer overflow in itertools.combinations.
 
@@ -2017,8 +2017,17 @@ product_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
         }
     }
 
-    assert(PyTuple_Check(args));
-    nargs = (repeat == 0) ? 0 : PyTuple_GET_SIZE(args);
+    assert(PyTuple_CheckExact(args));
+    if (repeat == 0) {
+        nargs = 0;
+    } else {
+        nargs = PyTuple_GET_SIZE(args);
+        if (repeat > PY_SSIZE_T_MAX/sizeof(Py_ssize_t) ||
+            nargs > PY_SSIZE_T_MAX/(repeat * sizeof(Py_ssize_t))) {
+            PyErr_SetString(PyExc_OverflowError, "repeat argument too large");
+            return NULL;
+        }
+    }
     npools = nargs * repeat;
 
     indices = PyMem_Malloc(npools * sizeof(Py_ssize_t));
@@ -3049,6 +3058,11 @@ permutations_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
         goto error;
     }
 
+    if (n > PY_SSIZE_T_MAX/sizeof(Py_ssize_t) ||
+        r > PY_SSIZE_T_MAX/sizeof(Py_ssize_t)) {
+        PyErr_SetString(PyExc_OverflowError, "parameters too large");
+        goto error;
+    }
     indices = PyMem_Malloc(n * sizeof(Py_ssize_t));
     cycles = PyMem_Malloc(r * sizeof(Py_ssize_t));
     if (indices == NULL || cycles == NULL) {