diff --git a/swh/storage/tests/test_api_client.py b/swh/storage/tests/test_api_client.py
--- a/swh/storage/tests/test_api_client.py
+++ b/swh/storage/tests/test_api_client.py
@@ -11,12 +11,12 @@
 from swh.core.tests.server_testing import ServerTestFixture
 from swh.storage.api.client import RemoteStorage
 from swh.storage.api.server import app
-from swh.storage.tests.test_storage import CommonTestStorage, \
-                                           StorageTestDbFixture
+from swh.storage.tests.test_storage import \
+    CommonTestStorage, CommonPropTestStorage, StorageTestDbFixture
 
 
-class TestRemoteStorage(CommonTestStorage, ServerTestFixture,
-                        StorageTestDbFixture, unittest.TestCase):
+class RemoteStorageFixture(ServerTestFixture, StorageTestDbFixture,
+                           unittest.TestCase):
     """Test the remote storage API.
 
     This class doesn't define any tests as we want identical
@@ -55,6 +55,15 @@
         super().tearDown()
         shutil.rmtree(self.storage_base)
 
+
+@pytest.mark.db
+class TestRemoteStorage(CommonTestStorage, RemoteStorageFixture):
     @pytest.mark.skip('refresh_stat_counters not available in the remote api.')
     def test_stat_counters(self):
         pass
+
+
+@pytest.mark.db
+@pytest.mark.property_based
+class PropTestRemoteStorage(CommonPropTestStorage, RemoteStorageFixture):
+    pass
diff --git a/swh/storage/tests/test_in_memory.py b/swh/storage/tests/test_in_memory.py
--- a/swh/storage/tests/test_in_memory.py
+++ b/swh/storage/tests/test_in_memory.py
@@ -8,7 +8,8 @@
 
 from swh.storage.in_memory import Storage
 
-from swh.storage.tests.test_storage import CommonTestStorage
+from swh.storage.tests.test_storage import \
+    CommonTestStorage, CommonPropTestStorage
 
 
 class TestInMemoryStorage(CommonTestStorage, unittest.TestCase):
@@ -29,3 +30,33 @@
     @pytest.mark.skip('postgresql-specific test')
     def test_skipped_content_add(self):
         pass
+
+
+@pytest.mark.db
+@pytest.mark.property_based
+class PropTestInMemoryStorage(CommonPropTestStorage, unittest.TestCase):
+    """Test the in-memory storage API
+
+    This class doesn't define any tests as we want identical
+    functionality between local and remote storage. All the tests are
+    therefore defined in CommonPropTestStorage.
+    """
+    def setUp(self):
+        super().setUp()
+        self.storage = Storage()
+
+    @pytest.mark.xfail(reason='not implemented yet')
+    def test_generate_content_get(self):
+        super().test_generate_content_get()
+
+    @pytest.mark.xfail(reason='not implemented yet')
+    def test_generate_content_get_range_limit_none(self):
+        super().test_generate_content_get_range_limit_none()
+
+    @pytest.mark.xfail(reason='not implemented yet')
+    def test_generate_content_get_range_no_limit(self):
+        super().test_generate_content_get_range_no_limit()
+
+    @pytest.mark.xfail(reason='not implemented yet')
+    def test_generate_content_get_range_limit(self):
+        super().test_generate_content_get_range_limit()
diff --git a/swh/storage/tests/test_storage.py b/swh/storage/tests/test_storage.py
--- a/swh/storage/tests/test_storage.py
+++ b/swh/storage/tests/test_storage.py
@@ -1850,9 +1850,7 @@
         self.assertEqual(m_by_provider, expected_results)
 
 
-@pytest.mark.db
-@pytest.mark.property_based
-class PropBasedTestStorage(StorageTestDbFixture, unittest.TestCase):
+class CommonPropTestStorage:
     def assert_contents_ok(self, expected_contents, actual_contents,
                            keys_to_check={'sha1', 'data'}):
         """Assert that a given list of contents matches on a given set of keys.
@@ -1972,6 +1970,7 @@
                                 keys_to_check)
 
 
+@pytest.mark.db
 class TestLocalStorage(CommonTestStorage, StorageTestDbFixture,
                        unittest.TestCase):
     """Test the local storage"""
@@ -2052,6 +2051,13 @@
         self.assertEqual(missing, [self.cont['sha1']])
 
 
+@pytest.mark.db
+@pytest.mark.property_based
+class PropTestLocalStorage(CommonPropTestStorage, StorageTestDbFixture,
+                           unittest.TestCase):
+    pass
+
+
 class AlteringSchemaTest(TestStorageData, StorageTestDbFixture,
                          unittest.TestCase):
     """This class is dedicated for the rare case where the schema needs to