diff --git a/docs/news.rst b/docs/news.rst
index fb5b16b2..3d431050 100644
--- a/docs/news.rst
+++ b/docs/news.rst
@@ -10,6 +10,9 @@ Release Notes
   values) is now delegated to ``setuptools>=57.0.0`` (#466).
   The package dependencies were updated to reflect this change.
 - Fixed potential DoS attack via the ``WHEEL_INFO_RE`` regular expression
+- Fixed ``ValueError: ZIP does not support timestamps before 1980`` when using
+  ``SOURCE_DATE_EPOCH=0`` or when on-disk timestamps are earlier than 1980-01-01. Such
+  timestamps are now changed to the minimum value before packaging.
 
 **0.37.1 (2021-12-22)**
 
diff --git a/src/wheel/wheelfile.py b/src/wheel/wheelfile.py
index b985774e..f55fc737 100644
--- a/src/wheel/wheelfile.py
+++ b/src/wheel/wheelfile.py
@@ -20,12 +20,14 @@
      -(?P<pyver>[^-]+?)-(?P<abi>[^-]+?)-(?P<plat>[^.]+?)\.whl$""",
     re.VERBOSE,
 )
+MINIMUM_TIMESTAMP = 315532800  # 1980-01-01 00:00:00 UTC
 
 
 def get_zipinfo_datetime(timestamp=None):
     # Some applications need reproducible .whl files, but they can't do this without
     # forcing the timestamp of the individual ZipInfo objects. See issue #143.
     timestamp = int(os.environ.get("SOURCE_DATE_EPOCH", timestamp or time.time()))
+    timestamp = max(timestamp, MINIMUM_TIMESTAMP)
     return time.gmtime(timestamp)[0:6]
 
 
diff --git a/tests/test_bdist_wheel.py b/tests/test_bdist_wheel.py
index 5ed9a41e..2a4d777a 100644
--- a/tests/test_bdist_wheel.py
+++ b/tests/test_bdist_wheel.py
@@ -202,3 +202,19 @@ def test_wheelfile_line_endings(wheel_paths):
             wheelfile = next(fn for fn in wf.filelist if fn.filename.endswith("WHEEL"))
             wheelfile_contents = wf.read(wheelfile)
             assert b"\r" not in wheelfile_contents
+
+
+def test_unix_epoch_timestamps(dummy_dist, monkeypatch, tmpdir):
+    monkeypatch.setenv("SOURCE_DATE_EPOCH", "0")
+    monkeypatch.chdir(dummy_dist)
+    subprocess.check_call(
+        [
+            sys.executable,
+            "setup.py",
+            "bdist_wheel",
+            "-b",
+            str(tmpdir),
+            "--universal",
+            "--build-number=2",
+        ]
+    )