diff --git a/CHANGELOG.md b/CHANGELOG.md
index 68c4cf34..0eafc6b6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,8 @@
 - Add `typing_extensions.get_annotations`, a backport of
   `inspect.get_annotations` that adds features specified
   by PEP 649. Patches by Jelle Zijlstra and Alex Waygood.
+- Copy the coroutine status of functions and methods wrapped
+  with `@typing_extensions.deprecated`. Patch by Sebastian Rittau.
 
 # Release 4.12.2 (June 7, 2024)
 
diff --git a/src/test_typing_extensions.py b/src/test_typing_extensions.py
index 868e7938..474c02cc 100644
--- a/src/test_typing_extensions.py
+++ b/src/test_typing_extensions.py
@@ -1,4 +1,5 @@
 import abc
+import asyncio
 import collections
 import collections.abc
 import contextlib
@@ -115,9 +116,15 @@
 # and adds PEP 695 to CPython's grammar
 TYPING_3_12_0 = sys.version_info[:3] >= (3, 12, 0)
 
+# @deprecated works differently in Python 3.12
+TYPING_3_12_ONLY = (3, 12) <= sys.version_info < (3, 13)
+
 # 3.13 drops support for the keyword argument syntax of TypedDict
 TYPING_3_13_0 = sys.version_info[:3] >= (3, 13, 0)
 
+# 3.13.0.rc1 fixes a problem with @deprecated
+TYPING_3_13_0_RC = sys.version_info[:4] >= (3, 13, 0, "candidate")
+
 # https://github.com/python/cpython/pull/27017 was backported into some 3.9 and 3.10
 # versions, but not all
 HAS_FORWARD_MODULE = "module" in inspect.signature(typing._type_check).parameters
@@ -850,6 +857,37 @@ def d(): pass
             isinstance(cell.cell_contents, deprecated) for cell in d.__closure__
         ))
 
+@deprecated("depr")
+def func():
+    pass
+
+@deprecated("depr")
+async def coro():
+    pass
+
+class Cls:
+    @deprecated("depr")
+    def func(self):
+        pass
+
+    @deprecated("depr")
+    async def coro(self):
+        pass
+
+class DeprecatedCoroTests(BaseTestCase):
+    def test_asyncio_iscoroutinefunction(self):
+        self.assertFalse(asyncio.coroutines.iscoroutinefunction(func))
+        self.assertFalse(asyncio.coroutines.iscoroutinefunction(Cls.func))
+        self.assertTrue(asyncio.coroutines.iscoroutinefunction(coro))
+        self.assertTrue(asyncio.coroutines.iscoroutinefunction(Cls.coro))
+
+    @skipUnless(TYPING_3_12_ONLY or TYPING_3_13_0_RC, "inspect.iscoroutinefunction works differently on Python < 3.12")
+    def test_inspect_iscoroutinefunction(self):
+        self.assertFalse(inspect.iscoroutinefunction(func))
+        self.assertFalse(inspect.iscoroutinefunction(Cls.func))
+        self.assertTrue(inspect.iscoroutinefunction(coro))
+        self.assertTrue(inspect.iscoroutinefunction(Cls.coro))
+
 
 class AnyTests(BaseTestCase):
     def test_can_subclass(self):
diff --git a/src/typing_extensions.py b/src/typing_extensions.py
index 8046dae1..1adc5823 100644
--- a/src/typing_extensions.py
+++ b/src/typing_extensions.py
@@ -2898,13 +2898,21 @@ def __init_subclass__(*args, **kwargs):
                 __init_subclass__.__deprecated__ = msg
                 return arg
             elif callable(arg):
+                import asyncio.coroutines
                 import functools
+                import inspect
 
                 @functools.wraps(arg)
                 def wrapper(*args, **kwargs):
                     warnings.warn(msg, category=category, stacklevel=stacklevel + 1)
                     return arg(*args, **kwargs)
 
+                if asyncio.coroutines.iscoroutinefunction(arg):
+                    if sys.version_info >= (3, 12):
+                        wrapper = inspect.markcoroutinefunction(wrapper)
+                    else:
+                        wrapper._is_coroutine = asyncio.coroutines._is_coroutine
+
                 arg.__deprecated__ = wrapper.__deprecated__ = msg
                 return wrapper
             else: