diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
index 810ec37..7093fc6 100644
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -489,6 +489,10 @@
         self.assertRaises(OSError, time.localtime, invalid_time_t)
         self.assertRaises(OSError, time.ctime, invalid_time_t)
 
+        # Issue #26669: check for localtime() failure
+        self.assertRaises(ValueError, time.localtime, float("nan"))
+        self.assertRaises(ValueError, time.ctime, float("nan"))
+
     def test_get_clock_info(self):
         clocks = ['clock', 'perf_counter', 'process_time', 'time']
         if hasattr(time, 'monotonic'):
@@ -823,6 +827,11 @@
                                 lambda secs: secs * SEC_TO_NS,
                                 value_filter=c_int_filter)
 
+        # test nan
+        for time_rnd, _ in ROUNDING_MODES:
+            with self.assertRaises(TypeError):
+                PyTime_FromSeconds(float('nan'))
+
     def test_FromSecondsObject(self):
         from _testcapi import PyTime_FromSecondsObject
 
@@ -834,6 +843,11 @@
             PyTime_FromSecondsObject,
             lambda ns: self.decimal_round(ns * SEC_TO_NS))
 
+        # test nan
+        for time_rnd, _ in ROUNDING_MODES:
+            with self.assertRaises(ValueError):
+                PyTime_FromSecondsObject(float('nan'), time_rnd)
+
     def test_AsSecondsDouble(self):
         from _testcapi import PyTime_AsSecondsDouble
 
@@ -847,6 +861,11 @@
                                 float_converter,
                                 NS_TO_SEC)
 
+        # test nan
+        for time_rnd, _ in ROUNDING_MODES:
+            with self.assertRaises(TypeError):
+                PyTime_AsSecondsDouble(float('nan'))
+
     def create_decimal_converter(self, denominator):
         denom = decimal.Decimal(denominator)
 
@@ -952,6 +971,11 @@
                                   self.create_converter(SEC_TO_US),
                                   value_filter=self.time_t_filter)
 
+         # test nan
+        for time_rnd, _ in ROUNDING_MODES:
+            with self.assertRaises(ValueError):
+                pytime_object_to_timeval(float('nan'), time_rnd)
+
     def test_object_to_timespec(self):
         from _testcapi import pytime_object_to_timespec
 
@@ -963,6 +987,11 @@
                                   self.create_converter(SEC_TO_NS),
                                   value_filter=self.time_t_filter)
 
+        # test nan
+        for time_rnd, _ in ROUNDING_MODES:
+            with self.assertRaises(ValueError):
+                pytime_object_to_timespec(float('nan'), time_rnd)
+
 
 if __name__ == "__main__":
     unittest.main()