diff --git a/jax/_src/ad_checkpoint.py b/jax/_src/ad_checkpoint.py
index df77ca3317ef..72b61af668b7 100644
--- a/jax/_src/ad_checkpoint.py
+++ b/jax/_src/ad_checkpoint.py
@@ -123,6 +123,14 @@ def save_and_offload_only_these_names(
     offload_src, offload_dst):
   names_which_can_be_saved = set(names_which_can_be_saved)
   names_which_can_be_offloaded = set(names_which_can_be_offloaded)
+  intersection = names_which_can_be_saved.intersection(names_which_can_be_offloaded)
+  if intersection:
+    raise ValueError(
+        "The names should be exclusive and should not intersect in"
+        " `names_which_can_be_saved` and `names_which_can_be_offloaded`. Got"
+        f" names_which_can_be_saved={names_which_can_be_saved},"
+        f" names_which_can_be_offloaded={names_which_can_be_offloaded} and the"
+        f" intersection={intersection}")
   def policy(prim, *_, **params):
     if prim is name_p and params['name'] in names_which_can_be_saved:
       return pe.Saveable
diff --git a/tests/memories_test.py b/tests/memories_test.py
index d3784ab59209..5c0cff5039d2 100644
--- a/tests/memories_test.py
+++ b/tests/memories_test.py
@@ -1124,6 +1124,12 @@ def test_remat_scan_jaxpr_offloadable(self):
     s = NamedSharding(mesh, P("x"))
     inp = jax.device_put(np_inp, s)
 
+    with self.assertRaisesRegex(
+        ValueError, "The names should be exclusive and should not intersect"):
+      jax.checkpoint_policies.save_and_offload_only_these_names(
+          names_which_can_be_saved=["y"], names_which_can_be_offloaded=["y", "w"],
+          offload_src="device", offload_dst="pinned_host")
+
     policy = jax.checkpoint_policies.save_and_offload_only_these_names(
         names_which_can_be_saved=["y"], names_which_can_be_offloaded=["z", "w"],
         offload_src='device', offload_dst='pinned_host')