diff --git a/chex/_src/asserts.py b/chex/_src/asserts.py
index 6c08c21..e950bf1 100644
--- a/chex/_src/asserts.py
+++ b/chex/_src/asserts.py
@@ -216,9 +216,30 @@ def assert_gpu_available(backend: Optional[str] = None) -> None:
     raise AssertionError(f"No GPU devices available in {jax.devices(backend)}.")
 
 
-@_static_assertion
-def assert_equal(first: Any, second: Any) -> None:
-  """Checks that the two objects are equal as determined by the `==` operator.
+def _assert_equal_static(first: Any, second: Any) -> None:
+  """Static (host) implementation of assert_equal."""
+  unittest.TestCase().assertEqual(first, second)
+
+
+def _assert_equal_jittable(first: Any, second: Any) -> Array:
+  """Jittable implementation of assert_equal for use with chexify."""
+  first_arr = jnp.asarray(first)
+  second_arr = jnp.asarray(second)
+  are_equal = jnp.array_equal(first_arr, second_arr)
+  checkify.check(are_equal, "Values are not equal: {first} != {second}.",
+                 first=first_arr, second=second_arr)
+  return are_equal
+
+
+assert_equal = _value_assertion(
+    assert_fn=_assert_equal_static,
+    jittable_assert_fn=_assert_equal_jittable,
+    name="assert_equal",
+)
+assert_equal.__doc__ = """Checks that the two objects are equal.
+
+  When used inside a ``@chex.chexify`` decorated function, this assertion
+  supports JAX tracing and can compare traced values.
 
   Arrays with more than one element cannot be compared.
   Use ``assert_trees_all_close`` to compare arrays.
@@ -230,7 +251,6 @@ def assert_equal(first: Any, second: Any) -> None:
   Raises:
     AssertionError: If not ``(first == second)``.
   """
-  unittest.TestCase().assertEqual(first, second)
 
 
 @_static_assertion
@@ -248,6 +268,20 @@ def assert_not_both_none(first: Any, second: Any) -> None:
     raise AssertionError(
         "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 not both arguments are non-None.
+
+  Args:
+    first: A first object.
+    second: A second object.
+
+  Raises:
+    AssertionError: If both ``first`` and ``second`` are not None.
+  """
+  if first is not None and second is not None:
+    raise AssertionError(
+        "At most one of the arguments may be different from `None`.")
 
 @_static_assertion
 def assert_exactly_one_is_none(first: Any, second: Any) -> None:
diff --git a/chex/_src/asserts_test.py b/chex/_src/asserts_test.py
index 6d5e9da..622dcc3 100644
--- a/chex/_src/asserts_test.py
+++ b/chex/_src/asserts_test.py
@@ -1860,7 +1860,15 @@ def test_assert_equal_fail(self, first, second):
     with self.assertRaises(AssertionError):
       asserts.assert_equal(first, second)
 
+class NotNoneAssertionsTest(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.assertRaises(AssertionError):
+            asserts.assert_not_both_not_none(1, 2)
 class IsDivisibleTest(parameterized.TestCase):
 
   def test_assert_is_divisible(self):