diff --git a/Doc/library/tarfile.rst b/Doc/library/tarfile.rst
index fc352e901f31dc..16578e7659458a 100644
--- a/Doc/library/tarfile.rst
+++ b/Doc/library/tarfile.rst
@@ -693,6 +693,12 @@ be finalized; only the internally used file object will be closed. See the
    :const:`None` the :class:`TarInfo` object will be excluded from the
    archive. See :ref:`tar-examples` for an example.
 
+   The file's last modification time is stored in the archive member's
+   :attr:`~TarInfo.mtime` as seconds since the epoch, without conversion to
+   local time.  Changing the process's time zone therefore does not itself
+   change the stored member timestamp, although the result can still vary if
+   the filesystem reports time-zone-dependent timestamps.
+
    .. versionchanged:: 3.2
       Added the *filter* parameter.
 
diff --git a/Doc/library/zipfile.rst b/Doc/library/zipfile.rst
index 98d2a5e5cdf00e..407f291e0fa67b 100644
--- a/Doc/library/zipfile.rst
+++ b/Doc/library/zipfile.rst
@@ -472,6 +472,14 @@ ZipFile objects
    given.
    The archive must be open with mode ``'w'``, ``'x'`` or ``'a'``.
 
+   The file's last modification time is converted to the current local time
+   and stored in the archive member's :attr:`~ZipInfo.date_time`.  Since ZIP
+   timestamps do not record a time zone, creating an archive from the same
+   file in different time zones can result in different stored timestamps.
+   To control the timestamp, create a :class:`ZipInfo` with an explicit
+   :attr:`~ZipInfo.date_time` and pass it with the file contents to
+   :meth:`writestr`.
+
    .. note::
 
       The ZIP file standard historically did not specify a metadata encoding,