There was a time when I used to work until late at night.
There was a period in my life when I traveled a lot.
1) There was a time when I used to work until late at night.
「夜遅くまで働いていた時期もあった。」
There was a time when を使って言うことができます。
2) There was a period in my life when I traveled a lot.
「旅行にしょっちゅう行っていた時期もあった。」
There was a period in my life when などとも言えます。
ご参考になれば幸いです!