diff --git a/pre_commit/clientlib.py b/pre_commit/clientlib.py
index 87679bfa6..0b8582bce 100644
--- a/pre_commit/clientlib.py
+++ b/pre_commit/clientlib.py
@@ -61,6 +61,7 @@ def _make_argparser(filenames_help: str) -> argparse.ArgumentParser:
     cfgv.Optional('files', check_string_regex, ''),
     cfgv.Optional('exclude', check_string_regex, '^$'),
     cfgv.Optional('types', cfgv.check_array(check_type_tag), ['file']),
+    cfgv.Optional('types_or', cfgv.check_array(check_type_tag), ['file']),
     cfgv.Optional('exclude_types', cfgv.check_array(check_type_tag), []),
 
     cfgv.Optional(
diff --git a/pre_commit/commands/run.py b/pre_commit/commands/run.py
index 0d335e285..1d6176df7 100644
--- a/pre_commit/commands/run.py
+++ b/pre_commit/commands/run.py
@@ -83,20 +83,30 @@ def by_types(
             self,
             names: Sequence[str],
             types: Collection[str],
+            types_or: Collection[str],
             exclude_types: Collection[str],
     ) -> List[str]:
-        types, exclude_types = frozenset(types), frozenset(exclude_types)
+        types, types_or, exclude_types = (
+            frozenset(types),
+            frozenset(types_or),
+            frozenset(exclude_types),
+        )
         ret = []
         for filename in names:
             tags = self._types_for_file(filename)
-            if tags >= types and not tags & exclude_types:
+            if tags >= types and not tags & exclude_types and tags & types_or:
                 ret.append(filename)
         return ret
 
     def filenames_for_hook(self, hook: Hook) -> Tuple[str, ...]:
         names = self.filenames
         names = filter_by_include_exclude(names, hook.files, hook.exclude)
-        names = self.by_types(names, hook.types, hook.exclude_types)
+        names = self.by_types(
+            names,
+            hook.types,
+            hook.types_or,
+            hook.exclude_types,
+        )
         return tuple(names)
 
     @classmethod
diff --git a/pre_commit/hook.py b/pre_commit/hook.py
index b65ac42b0..ea773942b 100644
--- a/pre_commit/hook.py
+++ b/pre_commit/hook.py
@@ -22,6 +22,7 @@ class Hook(NamedTuple):
     files: str
     exclude: str
     types: Sequence[str]
+    types_or: Sequence[str]
     exclude_types: Sequence[str]
     additional_dependencies: Sequence[str]
     args: Sequence[str]
diff --git a/pre_commit/meta_hooks/check_useless_excludes.py b/pre_commit/meta_hooks/check_useless_excludes.py
index db6865c6c..56d76d674 100644
--- a/pre_commit/meta_hooks/check_useless_excludes.py
+++ b/pre_commit/meta_hooks/check_useless_excludes.py
@@ -47,8 +47,12 @@ def check_useless_excludes(config_file: str) -> int:
             # the defaults applied during runtime
             hook = apply_defaults(hook, MANIFEST_HOOK_DICT)
             names = classifier.filenames
-            types, exclude_types = hook['types'], hook['exclude_types']
-            names = classifier.by_types(names, types, exclude_types)
+            types, types_or, exclude_types = (
+                hook['types'],
+                hook['types_or'],
+                hook['exclude_types'],
+            )
+            names = classifier.by_types(names, types, types_or, exclude_types)
             include, exclude = hook['files'], hook['exclude']
             if not exclude_matches_any(names, include, exclude):
                 print(
diff --git a/testing/resources/types_or_repo/.pre-commit-hooks.yaml b/testing/resources/types_or_repo/.pre-commit-hooks.yaml
new file mode 100644
index 000000000..a4ea920d6
--- /dev/null
+++ b/testing/resources/types_or_repo/.pre-commit-hooks.yaml
@@ -0,0 +1,6 @@
+-   id: python-cython-files
+    name: Python and Cython files
+    entry: bin/hook.sh
+    language: script
+    types: [file]
+    types_or: [python, cython]
diff --git a/testing/resources/types_or_repo/bin/hook.sh b/testing/resources/types_or_repo/bin/hook.sh
new file mode 100755
index 000000000..bdade5132
--- /dev/null
+++ b/testing/resources/types_or_repo/bin/hook.sh
@@ -0,0 +1,3 @@
+#!/usr/bin/env bash
+echo $@
+exit 1
diff --git a/tests/commands/run_test.py b/tests/commands/run_test.py
index 00b471282..34f3a3753 100644
--- a/tests/commands/run_test.py
+++ b/tests/commands/run_test.py
@@ -219,6 +219,19 @@ def test_types_hook_repository(cap_out, store, tempdir_factory):
         assert b'bar.notpy' not in printed
 
 
+def test_types_or_hook_repository(cap_out, store, tempdir_factory):
+    git_path = make_consuming_repo(tempdir_factory, 'types_or_repo')
+    with cwd(git_path):
+        stage_a_file('bar.notpy')
+        stage_a_file('bar.pxd')
+        stage_a_file('bar.py')
+        ret, printed = _do_run(cap_out, store, git_path, run_opts())
+        assert ret == 1
+        assert b'bar.notpy' not in printed
+        assert b'bar.pxd' in printed
+        assert b'bar.py' in printed
+
+
 def test_exclude_types_hook_repository(cap_out, store, tempdir_factory):
     git_path = make_consuming_repo(tempdir_factory, 'exclude_types_repo')
     with cwd(git_path):
diff --git a/tests/repository_test.py b/tests/repository_test.py
index 3d5093df6..8d771458f 100644
--- a/tests/repository_test.py
+++ b/tests/repository_test.py
@@ -901,6 +901,7 @@ def test_manifest_hooks(tempdir_factory, store):
             'post-commit', 'manual', 'post-checkout', 'push',
         ),
         types=['file'],
+        types_or=['file'],
         verbose=False,
     )