can a free member play in two tournaments?

Can I ?

online chess

I am signed up for two right now.Will I have to withdraw from one?

Official chess.com tournaments don't count towards your limit.

well The names of the tournaments are The Scandenavian Open. And the student and his game. The latter is a team tournament

yes

Hmm... can you post some links to the tournaments?

http://www.chess.com/tournament/scandinavian-open-spring-2013

http://www.chess.com/tournament/the-student-and-the-game-tourney

You can play two at the same time, you just cannot join one when are you still playing active games in another.

The system allowed you to register for the second tournament because you have no active games from the first tournament (even though you're moving on, it only checks for currently active games).

If you still had games going in the first tournament, you wouldn't have been allowed to even register for the second one.

Cannot see your name registered in 2nd link?

I withdrew because I thought that maybe when the second round in the other tournament started I would have to withdraw from one tournament and lose four games. So that won't happen?\

No, It sure wouldn't.