python
@@ -1180,21 +1180,32 @@ def _process_class(cls, init, repr, eq, order, unsafe_hash, frozen,
     if order:
         # Create and set the ordering methods.
         flds = [f for f in field_list if f.compare]
-        self_tuple = _tuple_str('self', flds)
-        other_tuple = _tuple_str('other', flds)
         for name, op in [('__lt__', '<'),
                          ('__le__', '<='),
                          ('__gt__', '>'),
                          ('__ge__', '>='),
                          ]:
             # Create a comparison function.  If the fields in the object are
-            # named 'x' and 'y', then self_tuple is the string
-            # '(self.x,self.y)' and other_tuple is the string
-            # '(other.x,other.y)'.
+            # named 'x' and 'y'.
+            # if self.x != other.x:
+            #   return self.x {op} other.x
+            # if self.y != other.y:
+            #   return self.y {op} other.y
+            # return {op.endswith("=")}
+            return_when_equal = f'   return {op.endswith("=")}'
             func_builder.add_fn(name,
                             ('self', 'other'),
-                            [ '  if other.__class__ is self.__class__:',
-                             f'   return {self_tuple}{op}{other_tuple}',
+                            [ '  if self is other:',
+                              # __eq__ has this self guard, add here for consistency
+                              return_when_equal,
+                              '  if other.__class__ is self.__class__:',
+                              *(
+                                f'   if self.{f.name} != other.{f.name}:\n'
+                                f'    return self.{f.name} {op} other.{f.name}'
+                                for f in flds
+                              ),
+                              # the instances are equal here, return constant
+                              return_when_equal,
                               '  return NotImplemented'],
                             overwrite_error='Consider using functools.total_ordering')
 

@@ -370,6 +370,16 @@ class C1:
         @dataclass(order=True)
         class C:
             pass
+
+        # Check "self" comparisons.
+        ref = C()
+        self.assertEqual(ref, ref)
+        self.assertLessEqual(ref, ref)
+        self.assertGreaterEqual(ref, ref)
+        self.assertFalse(ref != ref)
+        self.assertFalse(ref < ref)
+        self.assertFalse(ref > ref)
+
         self.assertLessEqual(C(), C())
         self.assertGreaterEqual(C(), C())
 
@@ -399,13 +409,62 @@ class C1:
         @dataclass(order=True)
         class C:
             x: int
+
+        # Check "self" comparisons.
+        ref = C(0)
+        self.assertEqual(ref, ref)
+        self.assertLessEqual(ref, ref)
+        self.assertGreaterEqual(ref, ref)
+        self.assertFalse(ref != ref)
+        self.assertFalse(ref < ref)
+        self.assertFalse(ref > ref)
+
         self.assertLess(C(0), C(1))
         self.assertLessEqual(C(0), C(1))
         self.assertLessEqual(C(1), C(1))
         self.assertGreater(C(1), C(0))
         self.assertGreaterEqual(C(1), C(0))
         self.assertGreaterEqual(C(1), C(1))
 
+        @dataclass(order=True)
+        class CFloat:
+            x: float
+
+        nan = float("nan")
+
+        # Check "self" comparisons.
+        ref = CFloat(nan)
+        self.assertEqual(ref, ref)
+        self.assertLessEqual(ref, ref)
+        self.assertGreaterEqual(ref, ref)
+        self.assertFalse(ref != ref)
+        self.assertFalse(ref < ref)
+        self.assertFalse(ref > ref)
+
+        self.assertNotEqual(CFloat(0.0), CFloat(nan))
+        self.assertNotEqual(CFloat(nan), CFloat(0.0))
+        self.assertNotEqual(CFloat(nan), CFloat(nan))
+
+        # gh-137658: Testing <, <=, == all return False with NaN
+        # Previously, <= would incorrectly return True on Python 3.13+ even though both < and == were False
+        for idx, fn in enumerate([lambda a, b: a < b,
+                                  lambda a, b: a <= b,
+                                  lambda a, b: a == b]):
+            with self.subTest(idx=idx):
+                self.assertFalse(fn(CFloat(0.0), CFloat(nan)))
+                self.assertFalse(fn(CFloat(nan), CFloat(0.0)))
+                self.assertFalse(fn(CFloat(nan), CFloat(nan)))
+
+        # gh-137658: Testing >, >=, == all return False with NaN
+        # Previously, >= would incorrectly return True on Python 3.13+ even though both > and == were False
+        for idx, fn in enumerate([lambda a, b: a > b,
+                                  lambda a, b: a >= b,
+                                  lambda a, b: a == b]):
+            with self.subTest(idx=idx):
+                self.assertFalse(fn(CFloat(0.0), CFloat(nan)))
+                self.assertFalse(fn(CFloat(nan), CFloat(0.0)))
+                self.assertFalse(fn(CFloat(nan), CFloat(nan)))
+
     def test_simple_compare(self):
         # Ensure that order=False is the default.
         @dataclass
@@ -460,6 +519,40 @@ class C:
                 self.assertTrue(fn(C(1, 0), C(0, 1)))
                 self.assertTrue(fn(C(1, 1), C(1, 0)))
 
+        @dataclass(order=True)
+        class CFloat:
+            x: float
+            y: float
+
+        nan = float("nan")
+
+        self.assertNotEqual(CFloat(0.0, nan), CFloat(nan, 0.0))
+        self.assertNotEqual(CFloat(0.0, 0.0), CFloat(nan, nan))
+        self.assertNotEqual(CFloat(0.0, nan), CFloat(nan, nan))
+        self.assertNotEqual(CFloat(nan, nan), CFloat(nan, nan))
+
+        # gh-137658: Testing <, <=, == all return False with NaN
+        # Previously, <= would incorrectly return True on Python 3.13+ even though both < and == were False
+        for idx, fn in enumerate([lambda a, b: a < b,
+                                  lambda a, b: a <= b,
+                                  lambda a, b: a == b]):
+            with self.subTest(idx=idx):
+                self.assertFalse(fn(CFloat(0.0, nan), CFloat(nan, 0.0)))
+                self.assertFalse(fn(CFloat(0.0, 0.0), CFloat(nan, nan)))
+                self.assertFalse(fn(CFloat(0.0, nan), CFloat(nan, nan)))
+                self.assertFalse(fn(CFloat(nan, nan), CFloat(nan, nan)))
+
+        # gh-137658: Testing >, >=, == all return False with NaN
+        # Previously, >= would incorrectly return True on Python 3.13+ even though both > and == were False
+        for idx, fn in enumerate([lambda a, b: a > b,
+                                  lambda a, b: a >= b,
+                                  lambda a, b: a == b]):
+            with self.subTest(idx=idx):
+                self.assertFalse(fn(CFloat(0.0, nan), CFloat(nan, 0.0)))
+                self.assertFalse(fn(CFloat(0.0, 0.0), CFloat(nan, nan)))
+                self.assertFalse(fn(CFloat(0.0, nan), CFloat(nan, nan)))
+                self.assertFalse(fn(CFloat(nan, nan), CFloat(nan, nan)))
+
     def test_compare_subclasses(self):
         # Comparisons fail for subclasses, even if no fields
         #  are added.

diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2025-08-11-19-26-46.gh-issue-137658.VaIFLO.rst b/Misc/NEWS.d/next/Core_and_Builtins/2025-08-11-19-26-46.gh-issue-137658.VaIFLO.rst
@@ -0,0 +1,2 @@
+Fix dataclass order method behaviors to align with the ``__eq__`` semantics
+change introduced in 3.13.
Original file line number	Diff line number	Diff line change
		@@ -0,0 +1,2 @@
		Fix dataclass order method behaviors to align with the ``__eq__`` semantics
		change introduced in 3.13.