diff --git a/docs/source/testing.rst b/docs/source/testing.rst
index f125c3a6f8..76fe47c40b 100644
--- a/docs/source/testing.rst
+++ b/docs/source/testing.rst
@@ -412,6 +412,16 @@ And we have these decorators that require the condition described by the marker.
 @require_torch_and_cuda
 ```
 
+Some decorators like ``@parametrized`` rewrite test names, therefore ``@require_*`` skip decorators have to be listed last for them to work correctly. Here is an example of the correct usage:
+
+.. code-block:: python
+
+    @parameterized.expand(...)
+    @require_multigpu
+    def test_integration_foo():
+    
+There is no problem whatsoever with ``@pytest.mark.parametrize`` (but it only works with non-unittests) - can use it in any order.
+
 This section will be expanded soon once our work in progress on those decorators is finished.
 
 Inside tests:
@@ -757,7 +767,7 @@ To run such tests set ``RUN_SLOW=1`` env var, e.g.:
 
     RUN_SLOW=1 pytest tests
     
-It's important that the decorator ``@slow`` appears last in the stack of decorators, as some decorators like ``parametrized`` may interfere with its normal functioning. Here is an example of the correct usage:
+Some decorators like ``@parametrized`` rewrite test names, therefore ``@slow`` and the rest of the skip decorators ``@require_*`` have to be listed last for them to work correctly. Here is an example of the correct usage:
 
 .. code-block:: python
 
diff --git a/src/transformers/testing_utils.py b/src/transformers/testing_utils.py
index d009ad3d5c..1dfbf66e51 100644
--- a/src/transformers/testing_utils.py
+++ b/src/transformers/testing_utils.py
@@ -62,8 +62,9 @@ def slow(test_case):
 
     """
     if not _run_slow_tests:
-        test_case = unittest.skip("test is slow")(test_case)
-    return test_case
+        return unittest.skip("test is slow")(test_case)
+    else:
+        return test_case
 
 
 def custom_tokenizers(test_case):
@@ -75,8 +76,9 @@ def custom_tokenizers(test_case):
     to a truthy value to run them.
     """
     if not _run_custom_tokenizers:
-        test_case = unittest.skip("test of custom tokenizers")(test_case)
-    return test_case
+        return unittest.skip("test of custom tokenizers")(test_case)
+    else:
+        return test_case
 
 
 def require_torch(test_case):
@@ -87,8 +89,9 @@ def require_torch(test_case):
 
     """
     if not _torch_available:
-        test_case = unittest.skip("test requires PyTorch")(test_case)
-    return test_case
+        return unittest.skip("test requires PyTorch")(test_case)
+    else:
+        return test_case
 
 
 def require_tf(test_case):
@@ -99,8 +102,9 @@ def require_tf(test_case):
 
     """
     if not _tf_available:
-        test_case = unittest.skip("test requires TensorFlow")(test_case)
-    return test_case
+        return unittest.skip("test requires TensorFlow")(test_case)
+    else:
+        return test_case
 
 
 def require_multigpu(test_case):
@@ -119,7 +123,8 @@ def require_multigpu(test_case):
 
     if torch.cuda.device_count() < 2:
         return unittest.skip("test requires multiple GPUs")(test_case)
-    return test_case
+    else:
+        return test_case
 
 
 def require_non_multigpu(test_case):
@@ -133,7 +138,8 @@ def require_non_multigpu(test_case):
 
     if torch.cuda.device_count() > 1:
         return unittest.skip("test requires 0 or 1 GPU")(test_case)
-    return test_case
+    else:
+        return test_case
 
 
 def require_torch_tpu(test_case):
@@ -142,8 +148,8 @@ def require_torch_tpu(test_case):
     """
     if not _torch_tpu_available:
         return unittest.skip("test requires PyTorch TPU")
-
-    return test_case
+    else:
+        return test_case
 
 
 if _torch_available:
@@ -154,9 +160,9 @@ else:
 
 
 def require_torch_and_cuda(test_case):
-    """Decorator marking a test that requires CUDA and PyTorch). """
+    """Decorator marking a test that requires CUDA and PyTorch. """
     if torch_device != "cuda":
-        return unittest.skip("test requires CUDA")
+        return unittest.skip("test requires CUDA")(test_case)
     else:
         return test_case
 
@@ -165,15 +171,17 @@ def require_datasets(test_case):
     """Decorator marking a test that requires datasets."""
 
     if not _datasets_available:
-        test_case = unittest.skip("test requires Datasets")(test_case)
-    return test_case
+        return unittest.skip("test requires `datasets`")(test_case)
+    else:
+        return test_case
 
 
 def require_faiss(test_case):
     """Decorator marking a test that requires faiss."""
     if not _faiss_available:
-        test_case = unittest.skip("test requires Faiss")(test_case)
-    return test_case
+        return unittest.skip("test requires `faiss`")(test_case)
+    else:
+        return test_case
 
 
 def get_tests_dir():
diff --git a/tests/test_skip_decorators.py b/tests/test_skip_decorators.py
new file mode 100644
index 0000000000..20a8541b88
--- /dev/null
+++ b/tests/test_skip_decorators.py
@@ -0,0 +1,120 @@
+# coding=utf-8
+# Copyright 2019-present, the HuggingFace Inc. team.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+#
+#
+# this test validates that we can stack skip decorators in groups and whether
+# they work correctly with other decorators
+#
+# since the decorators have already built their decision params (like checking
+# env[], we can't mock the env and test each of the combinations), so ideally
+# the following 4 should be run. But since we have different CI jobs running
+# different configs, all combinations should get covered
+#
+# USE_CUDA=1 RUN_SLOW=1 pytest -rA tests/test_skip_decorators.py
+# USE_CUDA=0 RUN_SLOW=1 pytest -rA tests/test_skip_decorators.py
+# USE_CUDA=0 RUN_SLOW=0 pytest -rA tests/test_skip_decorators.py
+# USE_CUDA=1 RUN_SLOW=0 pytest -rA tests/test_skip_decorators.py
+
+import os
+import unittest
+
+import pytest
+
+from parameterized import parameterized
+from transformers.testing_utils import require_torch, require_torch_and_cuda, slow, torch_device
+
+
+# skipping in unittest tests
+
+params = [(1,)]
+
+
+# test that we can stack our skip decorators with 3rd party decorators
+def check_slow():
+    run_slow = bool(os.getenv("RUN_SLOW", 0))
+    if run_slow:
+        assert True
+    else:
+        assert False, "should have been skipped"
+
+
+# test that we can stack our skip decorators
+def check_slow_torch_cuda():
+    run_slow = bool(os.getenv("RUN_SLOW", 0))
+    if run_slow and torch_device == "cuda":
+        assert True
+    else:
+        assert False, "should have been skipped"
+
+
+@require_torch
+class SkipTester(unittest.TestCase):
+    @slow
+    @require_torch_and_cuda
+    def test_2_skips_slow_first(self):
+        check_slow_torch_cuda()
+
+    @require_torch_and_cuda
+    @slow
+    def test_2_skips_slow_last(self):
+        check_slow_torch_cuda()
+
+    # The combination of any skip decorator, followed by parameterized fails to skip the tests
+    # 1. @slow manages to correctly skip `test_param_slow_first`
+    # 2. but then `parameterized` creates new tests, with a unique name for each parameter groups.
+    #    It has no idea that they are to be skipped and so they all run, ignoring @slow
+    # Therefore skip decorators must come after `parameterized`
+    #
+    # @slow
+    # @parameterized.expand(params)
+    # def test_param_slow_first(self, param=None):
+    #     check_slow()
+
+    # This works as expected:
+    # 1. `parameterized` creates new tests with unique names
+    # 2. each of them gets an opportunity to be skipped
+    @parameterized.expand(params)
+    @slow
+    def test_param_slow_last(self, param=None):
+        check_slow()
+
+
+# skipping in non-unittest tests
+# no problem at all here
+
+
+@slow
+@require_torch_and_cuda
+def test_pytest_2_skips_slow_first():
+    check_slow_torch_cuda()
+
+
+@require_torch_and_cuda
+@slow
+def test_pytest_2_skips_slow_last():
+    check_slow_torch_cuda()
+
+
+@slow
+@pytest.mark.parametrize("param", [1])
+def test_pytest_param_slow_first(param):
+    check_slow()
+
+
+@pytest.mark.parametrize("param", [1])
+@slow
+def test_pytest_param_slow_last(param):
+    check_slow()