diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index f623b15a0..ef3e0725b 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -9,6 +9,8 @@ Unreleased
 ----------
 
 .. vendor-insert-here
+- Fix the handling of malformed and missing ``Last-Modified`` headers in the
+  caching downloader. Thanks :user:`balihb`! (:issue:`275`)
 
 0.23.1
 ------
diff --git a/src/check_jsonschema/cachedownloader.py b/src/check_jsonschema/cachedownloader.py
index dc4d65066..5b6a26a7e 100644
--- a/src/check_jsonschema/cachedownloader.py
+++ b/src/check_jsonschema/cachedownloader.py
@@ -17,7 +17,6 @@ class FailedDownloadError(Exception):
 
 
 class CacheDownloader:
-    _LASTMOD_DEFAULT = "Sun, 01 Jan 1970 00:00:01 GMT"
     _LASTMOD_FMT = "%a, %d %b %Y %H:%M:%S %Z"
 
     # changed in v0.5.0
@@ -83,12 +82,15 @@ def _get_request(self) -> requests.Response:
             raise FailedDownloadError("encountered error during download") from e
 
     def _lastmod_from_response(self, response: requests.Response) -> float:
-        return time.mktime(
-            time.strptime(
-                response.headers.get("last-modified", self._LASTMOD_DEFAULT),
-                self._LASTMOD_FMT,
+        try:
+            return time.mktime(
+                time.strptime(response.headers["last-modified"], self._LASTMOD_FMT)
             )
-        )
+        # OverflowError: time outside of platform-specific bounds
+        # ValueError: malformed/unparseable
+        # LookupError: no such header
+        except (OverflowError, ValueError, LookupError):
+            return 0.0
 
     def _cache_hit(self, cachefile: str, response: requests.Response) -> bool:
         # no file? miss
diff --git a/tests/unit/test_cachedownloader.py b/tests/unit/test_cachedownloader.py
index 1f9fbb0f4..f26e08527 100644
--- a/tests/unit/test_cachedownloader.py
+++ b/tests/unit/test_cachedownloader.py
@@ -205,3 +205,66 @@ def test_cachedownloader_retries_on_bad_data(tmp_path, disable_cache):
         assert not f.exists()
     else:
         assert f.exists()
+
+
+@pytest.mark.parametrize("file_exists", (True, False))
+@pytest.mark.parametrize(
+    "failure_mode", ("header_missing", "header_malformed", "time_overflow")
+)
+def test_cachedownloader_handles_bad_lastmod_header(
+    monkeypatch, tmp_path, file_exists, failure_mode
+):
+    if failure_mode == "header_missing":
+        responses.add(
+            "GET",
+            "https://example.com/schema1.json",
+            headers={},
+            json={},
+            match_querystring=None,
+        )
+    elif failure_mode == "header_malformed":
+        responses.add(
+            "GET",
+            "https://example.com/schema1.json",
+            headers={"Last-Modified": "Jan 2000 00:00:01"},
+            json={},
+            match_querystring=None,
+        )
+    elif failure_mode == "time_overflow":
+        add_default_response()
+
+        def fake_mktime(*args):
+            raise OverflowError("uh-oh")
+
+        monkeypatch.setattr("time.mktime", fake_mktime)
+    else:
+        raise NotImplementedError
+
+    original_file_contents = b'{"foo": "bar"}'
+    f = tmp_path / "schema1.json"
+
+    if file_exists:
+        f.write_bytes(original_file_contents)
+    else:
+        assert not f.exists()
+
+    cd = CacheDownloader(
+        "https://example.com/schema1.json", filename=str(f), cache_dir=str(tmp_path)
+    )
+
+    # if the file already existed, it will not be overwritten by the cachedownloader
+    # so the returned value for both the downloader and a direct file read should be the
+    # original contents
+    if file_exists:
+        with cd.open() as fp:
+            assert fp.read() == original_file_contents
+        assert f.read_bytes() == original_file_contents
+    # otherwise, the file will have been created with new content
+    # both reads will show that new content
+    else:
+        with cd.open() as fp:
+            assert fp.read() == b"{}"
+        assert f.read_bytes() == b"{}"
+
+    # at the end, the file always exists on disk
+    assert f.exists()