diff --git a/Lib/test/lock_tests.py b/Lib/test/lock_tests.py
index fb11f4828957ff..1a41fd3f1ddb4d 100644
--- a/Lib/test/lock_tests.py
+++ b/Lib/test/lock_tests.py
@@ -557,6 +557,10 @@ def f():
         for r, dt in results2:
             self.assertTrue(r)
 
+    def test_nan_timeout(self):
+        evt = self.eventtype()
+        self.assertRaises(ValueError, evt.wait, float('nan'))
+
     def test_set_and_clear(self):
         # gh-57711: check that wait() returns true even when the event is
         # cleared before the waiting thread is woken up.
@@ -755,6 +759,14 @@ def f():
             # In practice, this implementation has no spurious wakeups.
             self.assertFalse(result)
 
+    def test_nan_timeout(self):
+        cond = self.condtype()
+        nan = float('nan')
+        with cond:
+            self.assertRaises(ValueError, cond.wait, nan)
+            self.assertRaises(ValueError, cond.wait_for, lambda: False, nan)
+            self.assertEqual(len(cond._waiters), 0)
+
     def test_waitfor(self):
         cond = self.condtype()
         state = 0
diff --git a/Lib/threading.py b/Lib/threading.py
index c03b0b5370c933..01274f1b857eee 100644
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -369,10 +369,11 @@ def wait(self, timeout=None):
                 waiter.acquire()
                 gotit = True
             else:
-                if timeout > 0:
-                    gotit = waiter.acquire(True, timeout)
-                else:
+                if timeout <= 0:
                     gotit = waiter.acquire(False)
+                else:
+                    # A NaN timeout is rejected by acquire().
+                    gotit = waiter.acquire(True, timeout)
             return gotit
         finally:
             self._acquire_restore(saved_state)
diff --git a/Misc/NEWS.d/next/Library/2026-10-22-18-30-00.gh-issue-160326.nAn7Tq.rst b/Misc/NEWS.d/next/Library/2026-10-22-18-30-00.gh-issue-160326.nAn7Tq.rst
new file mode 100644
index 00000000000000..4349a7380c377d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-10-22-18-30-00.gh-issue-160326.nAn7Tq.rst
@@ -0,0 +1,5 @@
+Raise :exc:`ValueError` for a NaN *timeout* in
+:meth:`threading.Condition.wait` and the blocking calls built on it, such as
+:meth:`threading.Event.wait`, :meth:`threading.Semaphore.acquire` and
+:meth:`queue.Queue.get`, instead of returning at once or looping without ever
+timing out.