diff --git a/Lib/functools.py b/Lib/functools.py
index eff6540c7f606e..69f32bd59c4801 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -1029,7 +1029,7 @@ def __init__(self, func):
         self.func = func
 
         import weakref # see comment in singledispatch function
-        self._method_cache = weakref.WeakKeyDictionary()
+        self._method_cache = weakref.WeakValueDictionary()
 
     def register(self, cls, method=None):
         """generic_method.register(cls, func) -> func
@@ -1039,15 +1039,12 @@ def register(self, cls, method=None):
         return self.dispatcher.register(cls, func=method)
 
     def __get__(self, obj, cls=None):
-        if self._method_cache is not None:
-            try:
-                _method = self._method_cache[obj]
-            except TypeError:
-                self._method_cache = None
-            except KeyError:
-                pass
-            else:
-                return _method
+        try:
+            _method = self._method_cache[id(obj)]
+        except KeyError:
+            pass
+        else:
+            return _method
 
         dispatch = self.dispatcher.dispatch
         funcname = getattr(self.func, '__name__', 'singledispatchmethod method')
@@ -1057,12 +1054,12 @@ def _method(*args, **kwargs):
                                 '1 positional argument')
             return dispatch(args[0].__class__).__get__(obj, cls)(*args, **kwargs)
 
+        _method.__self_reference = _method # create strong reference to _method. see gh-127751
         _method.__isabstractmethod__ = self.__isabstractmethod__
         _method.register = self.register
         update_wrapper(_method, self.func)
 
-        if self._method_cache is not None:
-            self._method_cache[obj] = _method
+        self._method_cache[id(obj)] = _method
 
         return _method
 
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index ffd2adb8665b45..d24294c7c8c837 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -3,6 +3,7 @@
 import collections
 import collections.abc
 import copy
+import gc
 from itertools import permutations
 import pickle
 from random import choice
@@ -3228,6 +3229,52 @@ def f(arg):
             def _(arg: undefined):
                 return "forward reference"
 
+    def test_singledispatchmethod_hash_comparision_equal(self):
+        from dataclasses import dataclass
+
+        @dataclass(frozen=True)
+        class A:
+            value: int
+
+            @functools.singledispatchmethod
+            def dispatch(self, x):
+                return id(self)
+
+        t1 = A(1)
+        t2 = A(1)
+
+        assert t1 == t2
+        assert id(t1) == t1.dispatch(2)
+        assert id(t2) == t2.dispatch(2) # gh-127750
+
+    def test_singledispatchmethod_object_references(self):
+        class ReferenceTest:
+            instance_counter = 0
+
+            def __init__(self):
+                ReferenceTest.instance_counter = ReferenceTest.instance_counter + 1
+
+            def __del__(self):
+                ReferenceTest.instance_counter = ReferenceTest.instance_counter - 1
+
+            @functools.singledispatchmethod
+            def go(self, item):
+                pass
+
+        assert ReferenceTest.instance_counter == 0
+        t=ReferenceTest()
+        assert ReferenceTest.instance_counter == 1
+        x = []
+        for ii in range(1000):
+            t = ReferenceTest()
+            t.go(ii)
+            x.append(t)
+        del t
+        del x
+        gc.collect()
+        assert ReferenceTest.instance_counter == 0
+
+
 class CachedCostItem:
     _cost = 1
 
diff --git a/Misc/NEWS.d/next/Library/2024-12-11-20-26-44.gh-issue-127750.8witaH.rst b/Misc/NEWS.d/next/Library/2024-12-11-20-26-44.gh-issue-127750.8witaH.rst
new file mode 100644
index 00000000000000..9ebf07e958e10d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-12-11-20-26-44.gh-issue-127750.8witaH.rst
@@ -0,0 +1 @@
+Update caching of :class:`functools.singledispatchmethod` to avoid collisions of objects which compare equal.