diff --git a/runtype/base_types.py b/runtype/base_types.py
index 53e319b..28146af 100644
--- a/runtype/base_types.py
+++ b/runtype/base_types.py
@@ -52,6 +52,11 @@ def __mul__(self, other: _Type):
     def __le__(self, other):
         return NotImplemented
 
+    def __hash__(self):
+        # __eq__ defined in eq()
+        return hash(type(self))
+
+
 class AnyType(Type):
     """Represents the Any type.
 
@@ -293,6 +298,10 @@ def ge(self, other):
 def eq(self, other):
     return NotImplemented
 
+@dp
+def eq(self: Type, other: Type):
+    return type(other) is type(self)
+
 @dp
 def eq(self: SumType, other: SumType):
     return self.types == other.types
diff --git a/runtype/pytypes.py b/runtype/pytypes.py
index b96a506..822f734 100644
--- a/runtype/pytypes.py
+++ b/runtype/pytypes.py
@@ -177,6 +177,15 @@ def cast_from(self, obj):
 
         return obj
 
+    def __eq__(self, other):
+        if type(other) != type(self):
+            return False
+        return self.kernel == other.kernel
+
+    def __hash__(self):
+        return hash((type(self), self.kernel))
+
+
 class TupleType(PythonType):
     def test_instance(self, obj, sampler=None):
         return isinstance(obj, tuple)