diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index cdfb13c759ed..e8bb3bffa858 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -12,6 +12,8 @@
 # Circular import; done in the function instead.
 # import mypy.solve
 from mypy.nodes import (
+    ARG_STAR,
+    ARG_STAR2,
     CONTRAVARIANT,
     COVARIANT,
     Decorator,
@@ -1291,6 +1293,16 @@ def are_parameters_compatible(
     right_star = right.var_arg()
     right_star2 = right.kw_arg()
 
+    # Treat "def _(*a: Any, **kw: Any) -> X" similarly to "Callable[..., X]"
+    if (
+        right.arg_kinds == [ARG_STAR, ARG_STAR2]
+        and right_star
+        and isinstance(get_proper_type(right_star.typ), AnyType)
+        and right_star2
+        and isinstance(get_proper_type(right_star2.typ), AnyType)
+    ):
+        return True
+
     # Match up corresponding arguments and check them for compatibility. In
     # every pair (argL, argR) of corresponding arguments from L and R, argL must
     # be "more general" than argR if L is to be a subtype of R.
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index a620c63ef58b..488531845be5 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -7136,6 +7136,16 @@ class B(A):  # E: Final class __main__.B has abstract attributes "foo"
 class C:
     class C1(XX): pass  # E: Name "XX" is not defined
 
+[case testArgsKwargsInheritance]
+from typing import Any
+
+class A(object):
+    def f(self, *args: Any, **kwargs: Any) -> int: ...
+
+class B(A):
+    def f(self, x: int) -> int: ...
+[builtins fixtures/dict.pyi]
+
 [case testClassScopeImports]
 class Foo:
     from mod import plain_function  # E: Unsupported class scoped import
diff --git a/test-data/unit/check-functions.test b/test-data/unit/check-functions.test
index a91b6099a02e..8793406f69e7 100644
--- a/test-data/unit/check-functions.test
+++ b/test-data/unit/check-functions.test
@@ -188,9 +188,9 @@ if int():
     ee_var = everywhere
 
 if int():
-    ee_var = specific_1 # The difference between Callable[..., blah] and one with a *args: Any, **kwargs: Any is that the ... goes loosely both ways.
+    ee_var = specific_1
 if int():
-    ee_def = specific_1 # E: Incompatible types in assignment (expression has type "Callable[[int, str], None]", variable has type "Callable[[VarArg(Any), KwArg(Any)], None]")
+    ee_def = specific_1
 
 [builtins fixtures/dict.pyi]
 
@@ -1787,7 +1787,7 @@ def f2(*args, **kwargs) -> int: pass
 d(f1)
 e(f2)
 d(f2)
-e(f1)  # E: Argument 1 to "e" has incompatible type "Callable[[VarArg(Any)], int]"; expected "Callable[[VarArg(Any), KwArg(Any)], int]"
+e(f1)
 
 [builtins fixtures/dict.pyi]
 
diff --git a/test-data/unit/check-modules.test b/test-data/unit/check-modules.test
index 60e95877336c..d83d0470c6b0 100644
--- a/test-data/unit/check-modules.test
+++ b/test-data/unit/check-modules.test
@@ -3160,7 +3160,7 @@ from test1 import aaaa  # E: Module "test1" has no attribute "aaaa"
 import b
 [file a.py]
 class Foo:
-    def frobnicate(self, *args, **kwargs): pass
+    def frobnicate(self, x, *args, **kwargs): pass
 [file b.py]
 from a import Foo
 class Bar(Foo):
@@ -3178,12 +3178,12 @@ class Bar(Foo):
 [out1]
 tmp/b.py:3: error: Signature of "frobnicate" incompatible with supertype "Foo"
 tmp/b.py:3: note:      Superclass:
-tmp/b.py:3: note:          def frobnicate(self, *args: Any, **kwargs: Any) -> Any
+tmp/b.py:3: note:          def frobnicate(self, x: Any, *args: Any, **kwargs: Any) -> Any
 tmp/b.py:3: note:      Subclass:
 tmp/b.py:3: note:          def frobnicate(self) -> None
 [out2]
 tmp/b.py:3: error: Signature of "frobnicate" incompatible with supertype "Foo"
 tmp/b.py:3: note:      Superclass:
-tmp/b.py:3: note:          def frobnicate(self, *args: Any, **kwargs: Any) -> Any
+tmp/b.py:3: note:          def frobnicate(self, x: Any, *args: Any, **kwargs: Any) -> Any
 tmp/b.py:3: note:      Subclass:
 tmp/b.py:3: note:          def frobnicate(self, *args: Any) -> None