diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 58954ef88..c02a0632b 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -2,7 +2,7 @@
 # See https://pre-commit.com/hooks.html for more hooks
 repos:
   - repo: https://github.com/pre-commit/pre-commit-hooks
-    rev: v4.6.0
+    rev: v5.0.0
     hooks:
       - id: check-symlinks
       - id: destroyed-symlinks
@@ -35,7 +35,7 @@ repos:
           - --show-source
           - --statistics
   - repo: https://github.com/asottile/pyupgrade
-    rev: v3.17.0
+    rev: v3.19.1
     hooks:
       - id: pyupgrade
         args: ["--py38-plus"]
@@ -44,7 +44,7 @@ repos:
     hooks:
       - id: isort
   - repo: https://github.com/python/black
-    rev: 24.8.0
+    rev: 24.10.0
     hooks:
       - id: black
   - repo: https://github.com/pycqa/pydocstyle
diff --git a/gymnasium/wrappers/stateful_observation.py b/gymnasium/wrappers/stateful_observation.py
index 17dec84e8..230ac9b49 100644
--- a/gymnasium/wrappers/stateful_observation.py
+++ b/gymnasium/wrappers/stateful_observation.py
@@ -198,9 +198,18 @@ class TimeAwareObservation(
         if env.spec is not None and env.spec.max_episode_steps is not None:
             self.max_timesteps = env.spec.max_episode_steps
         else:
-            raise ValueError(
-                "The environment must be wrapped by a TimeLimit wrapper or the spec specify a `max_episode_steps`."
-            )
+            # else we need to loop through the environment stack to check if a `TimeLimit` wrapper exists
+            wrapped_env = env
+            while isinstance(wrapped_env, gym.Wrapper):
+                if isinstance(wrapped_env, gym.wrappers.TimeLimit):
+                    self.max_timesteps = wrapped_env._max_episode_steps
+                    break
+                wrapped_env = wrapped_env.env
+
+            if not isinstance(wrapped_env, gym.wrappers.TimeLimit):
+                raise ValueError(
+                    "The environment must be wrapped by a TimeLimit wrapper or the spec specify a `max_episode_steps`."
+                )
 
         self.timesteps: int = 0
 
diff --git a/tests/wrappers/test_time_aware_observation.py b/tests/wrappers/test_time_aware_observation.py
index 0fd0ae23e..33a9ed379 100644
--- a/tests/wrappers/test_time_aware_observation.py
+++ b/tests/wrappers/test_time_aware_observation.py
@@ -1,12 +1,16 @@
 """Test suite for TimeAwareObservation wrapper."""
 
+import re
+import warnings
+
 import numpy as np
 import pytest
 
 import gymnasium as gym
 from gymnasium import spaces
+from gymnasium.envs.classic_control import CartPoleEnv
 from gymnasium.spaces import Box, Dict, Tuple
-from gymnasium.wrappers import TimeAwareObservation
+from gymnasium.wrappers import TimeAwareObservation, TimeLimit
 from tests.testing_env import GenericTestEnv
 
 
@@ -41,6 +45,25 @@ def test_default(env_id):
     assert wrapped_obs.shape[0] == obs.shape[0] + 1
 
 
+def test_no_spec():
+    env = CartPoleEnv()
+
+    with pytest.raises(
+        ValueError,
+        match=re.escape(
+            "The environment must be wrapped by a TimeLimit wrapper or the spec specify a `max_episode_steps`."
+        ),
+    ):
+        TimeAwareObservation(env)
+
+    env = TimeLimit(env, 100)
+    with warnings.catch_warnings(record=True) as caught_warnings:
+        env = TimeAwareObservation(env)
+
+        assert env.max_timesteps == 100
+    assert len(caught_warnings) == 0
+
+
 def test_no_flatten():
     """Test the TimeAwareObservation wrapper without flattening the space."""
     env = GenericTestEnv(observation_space=Box(0, 1))