diff --git a/chex/__init__.py b/chex/__init__.py
index 0da55ec..c0ce4c0 100644
--- a/chex/__init__.py
+++ b/chex/__init__.py
@@ -33,6 +33,7 @@
 from chex._src.asserts import assert_is_divisible
 from chex._src.asserts import assert_max_traces
 from chex._src.asserts import assert_not_both_none
+from chex._src.asserts import assert_not_both_not_none
 from chex._src.asserts import assert_numerical_grads
 from chex._src.asserts import assert_rank
 from chex._src.asserts import assert_scalar
@@ -138,6 +139,7 @@
     "assert_is_divisible",
     "assert_max_traces",
     "assert_not_both_none",
+    "assert_not_both_not_none",
     "assert_numerical_grads",
     "assert_rank",
     "assert_scalar",
diff --git a/chex/_src/asserts.py b/chex/_src/asserts.py
index 6c08c21..6230d3f 100644
--- a/chex/_src/asserts.py
+++ b/chex/_src/asserts.py
@@ -249,6 +249,22 @@ def assert_not_both_none(first: Any, second: Any) -> None:
         "At least one of the arguments must be different from `None`.")
 
 
+@_static_assertion
+def assert_not_both_not_none(first: Any, second: Any) -> None:
+  """Checks that at most one of the arguments is not `None`.
+
+  Args:
+    first: A first object.
+    second: A second object.
+
+  Raises:
+    AssertionError: If ``(first is not None) and (second is not None)``.
+  """
+  if first is not None and second is not None:
+    raise AssertionError(
+        "At most one of the arguments must be different from `None`.")
+
+
 @_static_assertion
 def assert_exactly_one_is_none(first: Any, second: Any) -> None:
   """Checks that one and only one of the arguments is `None`.
diff --git a/chex/_src/asserts_test.py b/chex/_src/asserts_test.py
index 6d5e9da..1b33562 100644
--- a/chex/_src/asserts_test.py
+++ b/chex/_src/asserts_test.py
@@ -1871,6 +1871,28 @@ def test_assert_is_divisible_fail(self):
       asserts.assert_is_divisible(7, 3)
 
 
+
+class NoneCheckTest(parameterized.TestCase):
+
+  def test_assert_not_both_not_none(self):
+    asserts.assert_not_both_not_none(None, None)
+    asserts.assert_not_both_not_none(1, None)
+    asserts.assert_not_both_not_none(None, 1)
+
+    with self.assertRaisesRegex(AssertionError,
+                                _get_err_regex('At most one')):
+      asserts.assert_not_both_not_none(1, 1)
+
+  def test_assert_not_both_none(self):
+    asserts.assert_not_both_none(1, None)
+    asserts.assert_not_both_none(None, 1)
+    asserts.assert_not_both_none(1, 1)
+
+    with self.assertRaisesRegex(AssertionError,
+                                _get_err_regex('At least one')):
+      asserts.assert_not_both_none(None, None)
+
+
 if __name__ == '__main__':
   jax.config.update('jax_numpy_rank_promotion', 'raise')
   absltest.main()