diff --git a/freezegun/api.py b/freezegun/api.py
index 81d4da17..3dd83b52 100644
--- a/freezegun/api.py
+++ b/freezegun/api.py
@@ -295,7 +295,8 @@ def datetime_to_fakedatetime(datetime):
                         datetime.minute,
                         datetime.second,
                         datetime.microsecond,
-                        datetime.tzinfo)
+                        datetime.tzinfo,
+                        fold=datetime.fold)
 
 
 def date_to_fakedate(date):
@@ -385,9 +386,14 @@ def timestamp(self):
     def now(cls, tz=None):
         now = cls._time_to_freeze() or real_datetime.now()
         if tz:
-            result = tz.fromutc(now.replace(tzinfo=tz)) + cls._tz_offset()
+            result = tz.fromutc(now.replace(tzinfo=tz))
         else:
-            result = now + cls._tz_offset()
+            result = now
+
+        # Add the _tz_offset only if it's non-zero to preserve fold
+        if cls._tz_offset():
+            result += cls._tz_offset()
+
         return datetime_to_fakedatetime(result)
 
     def date(self):
diff --git a/tests/test_operations.py b/tests/test_operations.py
index 303a1dc8..f61b8fb6 100644
--- a/tests/test_operations.py
+++ b/tests/test_operations.py
@@ -1,5 +1,6 @@
 import datetime
 from freezegun import freeze_time
+from dateutil import tz
 from dateutil.relativedelta import relativedelta
 from datetime import timedelta, tzinfo
 from tests import utils
@@ -63,6 +64,15 @@ def test_datetime_timezone_real():
     assert now.utcoffset() == timedelta(0, 60 * 60 * 5)
 
 
+@freeze_time("2021-10-31 02:30:00+01:00")  # This will have fold set to 1
+def test_datetime_timezone_real_fold():
+    vienna = tz.gettz("Europe/Vienna")
+    now = datetime.datetime.now(tz=vienna)
+    assert now == datetime.datetime(2021, 10, 31, 2, 30, tzinfo=vienna)
+    assert now.utcoffset() == timedelta(0, 60 * 60 * 1)
+    assert now.fold == 1
+
+
 @freeze_time("2012-01-14 2:00:00", tz_offset=-4)
 def test_datetime_timezone_real_with_offset():
     now = datetime.datetime.now(tz=GMT5())
@@ -70,6 +80,16 @@ def test_datetime_timezone_real_with_offset():
     assert now.utcoffset() == timedelta(0, 60 * 60 * 5)
 
 
+@freeze_time("2021-10-31 06:30:00+01:00", tz_offset=-4)
+def test_datetime_timezone_real_with_offset_fold():
+    vienna = tz.gettz("Europe/Vienna")
+    now = datetime.datetime.now(tz=vienna)
+    assert now == datetime.datetime(2021, 10, 31, 2, 30, tzinfo=vienna)
+    # Because of adding the tz_offset timedelta, fold information is lost
+    assert now.utcoffset() == timedelta(0, 60 * 60 * 2)
+    assert now.fold == 0
+
+
 @freeze_time("2012-01-14 00:00:00")
 def test_astimezone():
     now = datetime.datetime.now(tz=GMT5())