diff --git a/Lib/test/test_genericalias.py b/Lib/test/test_genericalias.py
index ccf40b1..fd024dc 100644
--- a/Lib/test/test_genericalias.py
+++ b/Lib/test/test_genericalias.py
@@ -369,6 +369,27 @@ def __call__(self):
             self.assertEqual(c1.__args__, c2.__args__)
             self.assertEqual(hash(c1.__args__), hash(c2.__args__))
 
+        with self.subTest("Testing ParamSpec uses"):
+            P = typing.ParamSpec('P')
+            C1 = Callable[P, T]
+            # substitution
+            self.assertEqual(C1[int, str], Callable[[int], str])
+            self.assertEqual(C1[[int, str], str], Callable[[int, str], str])
+            self.assertEqual(repr(C1).split(".")[-1], "Callable[~P, ~T]")
+            self.assertEqual(repr(C1[int, str]).split(".")[-1], "Callable[[int], str]")
+
+            C2 = Callable[P, int]
+            # special case in PEP 612 where
+            # X[int, str, float] == X[[int, str, float]]
+            self.assertEqual(C2[int, str, float], C2[[int, str, float]])
+            self.assertEqual(repr(C2).split(".")[-1], "Callable[~P, int]")
+            self.assertEqual(repr(C2[int, str]).split(".")[-1], "Callable[[int, str], int]")
+
+        with self.subTest("Testing Concatenate uses"):
+            P = typing.ParamSpec('P')
+            C1 = Callable[typing.Concatenate[int, P], int]
+            self.assertEqual(repr(C1), "collections.abc.Callable"
+                                       "[typing.Concatenate[int, ~P], int]")
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index 8e86e76..c340c8a 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -25,6 +25,7 @@
 from typing import Pattern, Match
 from typing import Annotated, ForwardRef
 from typing import TypeAlias
+from typing import ParamSpec, Concatenate
 import abc
 import typing
 import weakref
@@ -1130,10 +1131,6 @@ class P(PR[int, T], Protocol[T]):
             PR[int]
         with self.assertRaises(TypeError):
             P[int, str]
-        with self.assertRaises(TypeError):
-            PR[int, 1]
-        with self.assertRaises(TypeError):
-            PR[int, ClassVar]
 
         class C(PR[int, T]): pass
 
@@ -1155,8 +1152,6 @@ class P(PR[int, str], Protocol):
         self.assertIsSubclass(P, PR)
         with self.assertRaises(TypeError):
             PR[int]
-        with self.assertRaises(TypeError):
-            PR[int, 1]
 
         class P1(Protocol, Generic[T]):
             def bar(self, x: T) -> str: ...
@@ -1175,8 +1170,6 @@ def bar(self, x: str) -> str:
                 return x
 
         self.assertIsInstance(Test(), PSub)
-        with self.assertRaises(TypeError):
-            PR[int, ClassVar]
 
     def test_init_called(self):
         T = TypeVar('T')
@@ -1746,8 +1739,6 @@ def test_extended_generic_rules_eq(self):
         self.assertEqual(typing.Iterable[Tuple[T, T]][T], typing.Iterable[Tuple[T, T]])
         with self.assertRaises(TypeError):
             Tuple[T, int][()]
-        with self.assertRaises(TypeError):
-            Tuple[T, U][T, ...]
 
         self.assertEqual(Union[T, int][int], int)
         self.assertEqual(Union[T, U][int, Union[int, str]], Union[int, str])
@@ -1759,10 +1750,6 @@ class Derived(Base): ...
 
         self.assertEqual(Callable[[T], T][KT], Callable[[KT], KT])
         self.assertEqual(Callable[..., List[T]][int], Callable[..., List[int]])
-        with self.assertRaises(TypeError):
-            Callable[[T], U][..., int]
-        with self.assertRaises(TypeError):
-            Callable[[T], U][[], int]
 
     def test_extended_generic_rules_repr(self):
         T = TypeVar('T')
@@ -4243,6 +4230,111 @@ def test_cannot_subscript(self):
             TypeAlias[int]
 
 
+class ParamSpecTests(BaseTestCase):
+
+    def test_basic_plain(self):
+        P = ParamSpec('P')
+        self.assertEqual(P, P)
+        self.assertIsInstance(P, ParamSpec)
+
+    def test_valid_uses(self):
+        P = ParamSpec('P')
+        T = TypeVar('T')
+        C1 = Callable[P, int]
+        self.assertEqual(C1.__args__, (P, int))
+        self.assertEqual(C1.__parameters__, (P,))
+        C2 = Callable[P, T]
+        self.assertEqual(C2.__args__, (P, T))
+        self.assertEqual(C2.__parameters__, (P, T))
+        # Test collections.abc.Callable too.
+        C3 = collections.abc.Callable[P, int]
+        self.assertEqual(C3.__args__, (P, int))
+        self.assertEqual(C3.__parameters__, (P,))
+        C4 = collections.abc.Callable[P, T]
+        self.assertEqual(C4.__args__, (P, T))
+        self.assertEqual(C4.__parameters__, (P, T))
+
+        # ParamSpec instances should also have args and kwargs attributes.
+        self.assertIn('args', dir(P))
+        self.assertIn('kwargs', dir(P))
+        P.args
+        P.kwargs
+
+    def test_user_generics(self):
+        T = TypeVar("T")
+        P = ParamSpec("P")
+        P_2 = ParamSpec("P_2")
+
+        class X(Generic[T, P]):
+            f: Callable[P, int]
+            x: T
+        G1 = X[int, P_2]
+        self.assertEqual(G1.__args__, (int, P_2))
+        self.assertEqual(G1.__parameters__, (P_2,))
+
+        G2 = X[int, Concatenate[int, P_2]]
+        self.assertEqual(G2.__args__, (int, Concatenate[int, P_2]))
+        self.assertEqual(G2.__parameters__, (P_2,))
+
+        G3 = X[int, [int, bool]]
+        self.assertEqual(G3.__args__, (int, (int, bool)))
+        self.assertEqual(G3.__parameters__, ())
+
+        G4 = X[int, ...]
+        self.assertEqual(G4.__args__, (int, Ellipsis))
+        self.assertEqual(G4.__parameters__, ())
+
+        class Z(Generic[P]):
+            f: Callable[P, int]
+
+        G5 = Z[[int, str, bool]]
+        self.assertEqual(G5.__args__, ((int, str, bool),))
+        self.assertEqual(G5.__parameters__, ())
+
+        G6 = Z[int, str, bool]
+        self.assertEqual(G6.__args__, ((int, str, bool),))
+        self.assertEqual(G6.__parameters__, ())
+
+        # G5 and G6 should be equivalent according to the PEP
+        self.assertEqual(G5.__args__, G6.__args__)
+        self.assertEqual(G5.__origin__, G6.__origin__)
+        self.assertEqual(G5.__parameters__, G6.__parameters__)
+        self.assertEqual(G5, G6)
+
+    def test_var_substitution(self):
+        T = TypeVar("T")
+        P = ParamSpec("P")
+        C1 = Callable[P, T]
+        self.assertEqual(C1[int, str], Callable[[int], str])
+        self.assertEqual(C1[[int, str, dict], float], Callable[[int, str, dict], float])
+
+
+class ConcatenateTests(BaseTestCase):
+    def test_basics(self):
+        P = ParamSpec('P')
+        class MyClass: ...
+        c = Concatenate[MyClass, P]
+        self.assertNotEqual(c, Concatenate)
+
+    def test_valid_uses(self):
+        P = ParamSpec('P')
+        T = TypeVar('T')
+        C1 = Callable[Concatenate[int, P], int]
+        self.assertEqual(C1.__args__, (Concatenate[int, P], int))
+        self.assertEqual(C1.__parameters__, (P,))
+        C2 = Callable[Concatenate[int, T, P], T]
+        self.assertEqual(C2.__args__, (Concatenate[int, T, P], T))
+        self.assertEqual(C2.__parameters__, (T, P))
+
+        # Test collections.abc.Callable too.
+        C3 = collections.abc.Callable[Concatenate[int, P], int]
+        self.assertEqual(C3.__args__, (Concatenate[int, P], int))
+        self.assertEqual(C3.__parameters__, (P,))
+        C4 = collections.abc.Callable[Concatenate[int, T, P], T]
+        self.assertEqual(C4.__args__, (Concatenate[int, T, P], T))
+        self.assertEqual(C4.__parameters__, (T, P))
+
+
 class AllTests(BaseTestCase):
     """Tests for __all__."""