diff --git a/sdks/python/apache_beam/transforms/core.py b/sdks/python/apache_beam/transforms/core.py
index 5f68294972c6..6245bb7703fb 100644
--- a/sdks/python/apache_beam/transforms/core.py
+++ b/sdks/python/apache_beam/transforms/core.py
@@ -585,7 +585,7 @@ def default_type_hints(self):
   # TODO(sourabhbajaj): Do we want to remove the responsibility of these from
   # the DoFn or maybe the runner
   def infer_output_type(self, input_type):
-    # TODO(robertwb): Side inputs types.
+    # TODO(BEAM-8247): Side inputs types.
     # TODO(robertwb): Assert compatibility with input type hint?
     return self._strip_output_annotations(
         trivial_inference.infer_return_type(self.process, [input_type]))
@@ -618,7 +618,9 @@ def _fn_takes_side_inputs(fn):
     # We can't tell; maybe it does.
     return True
 
-  return len(signature.parameters) > 1
+  return (len(signature.parameters) > 1 or
+          any(p.kind == p.VAR_POSITIONAL or p.kind == p.VAR_KEYWORD
+              for p in signature.parameters.values()))
 
 
 class CallableWrapperDoFn(DoFn):
diff --git a/sdks/python/apache_beam/typehints/typed_pipeline_test.py b/sdks/python/apache_beam/typehints/typed_pipeline_test.py
index 82c4a63c4225..48129ecbec56 100644
--- a/sdks/python/apache_beam/typehints/typed_pipeline_test.py
+++ b/sdks/python/apache_beam/typehints/typed_pipeline_test.py
@@ -221,9 +221,52 @@ def repeat(s, *times):
     result = ['a', 'bb', 'c'] | beam.Map(repeat, 3)
     self.assertEqual(['aaa', 'bbbbbb', 'ccc'], sorted(result))
 
-  # TODO(robertwb): Support partially defined varargs.
-  # with self.assertRaises(typehints.TypeCheckError):
-  #   ['a', 'bb', 'c'] | beam.Map(repeat, 'z')
+    if sys.version_info >= (3,):
+      with self.assertRaisesRegexp(
+          typehints.TypeCheckError,
+          r'requires Tuple\[int, ...\] but got Tuple\[str, ...\]'):
+        ['a', 'bb', 'c'] | beam.Map(repeat, 'z')
+
+  def test_var_positional_only_side_input_hint(self):
+    # Test that a lambda that accepts only a VAR_POSITIONAL can accept
+    # side-inputs.
+    # TODO(BEAM-8247): There's a bug with trivial_inference inferring the output
+    #   type when side-inputs are used (their type hints are not passed). Remove
+    #   with_output_types(...) when this bug is fixed.
+    result = (['a', 'b', 'c']
+              | beam.Map(lambda *args: args, 5).with_input_types(int, str)
+              .with_output_types(typehints.Tuple[str, int]))
+    self.assertEqual([('a', 5), ('b', 5), ('c', 5)], sorted(result))
+
+    # Type hint order doesn't matter for VAR_POSITIONAL.
+    result = (['a', 'b', 'c']
+              | beam.Map(lambda *args: args, 5).with_input_types(int, str)
+              .with_output_types(typehints.Tuple[str, int]))
+    self.assertEqual([('a', 5), ('b', 5), ('c', 5)], sorted(result))
+
+    if sys.version_info >= (3,):
+      with self.assertRaisesRegexp(
+          typehints.TypeCheckError,
+          r'requires Tuple\[Union\[int, str\], ...\] but got '
+          r'Tuple\[Union\[float, int\], ...\]'):
+        _ = [1.2] | beam.Map(lambda *_: 'a', 5).with_input_types(int, str)
+
+  def test_var_keyword_side_input_hint(self):
+    # Test that a lambda that accepts a VAR_KEYWORD can accept
+    # side-inputs.
+    result = (['a', 'b', 'c']
+              | beam.Map(lambda e, **kwargs: (e, kwargs), kw=5)
+              .with_input_types(str, ignored=int))
+    self.assertEqual([('a', {'kw': 5}), ('b', {'kw': 5}), ('c', {'kw': 5})],
+                     sorted(result))
+
+    if sys.version_info >= (3,):
+      with self.assertRaisesRegexp(
+          typehints.TypeCheckError,
+          r'requires Dict\[str, str\] but got Dict\[str, int\]'):
+        _ = (['a', 'b', 'c']
+             | beam.Map(lambda e, **_: 'a', kw=5)
+             .with_input_types(str, ignored=str))
 
   def test_deferred_side_inputs(self):
     @typehints.with_input_types(str, int)