diff --git a/cmd/linkcheck/links.go b/cmd/linkcheck/links.go
index d83b3ae7bac..4930b9bb33b 100644
--- a/cmd/linkcheck/links.go
+++ b/cmd/linkcheck/links.go
@@ -129,7 +129,10 @@ func newWalkFunc(invalidLink *bool, client *http.Client) filepath.WalkFunc {
 				if err != nil {
 					break
 				}
-				if resp.StatusCode == http.StatusTooManyRequests {
+				// This header is used in 301, 429 and 503.
+				// https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Retry-After
+				// And Go client will follow redirects automatically so the 301 check is probably unnecessary.
+				if resp.StatusCode == http.StatusTooManyRequests || resp.StatusCode == http.StatusServiceUnavailable {
 					retryAfter := resp.Header.Get("Retry-After")
 					if seconds, err := strconv.Atoi(retryAfter); err != nil {
 						backoff = seconds + 10