If you're referring to saving games to memory cards then it can be done. You cannot save Playstation1 games to Playstation2 memory cards. You need a Playstation1 memory card to save Playstation1 games. Although the game and card will work in the Playstation2. Playstation2 games cannot be saved on it.
I have a Playstation 2 and while you can use Playstation 1 games in the system you cannot use a Playstation 1 game card for saving games. You can however save Playstation 1 games on a Playstation2 card.