Since I've never played one... I was wondering, Can you offer a draw or resign during your oponent's turn in OTB tournaments?

Wether it's normal or not... what do you think about it?. I don't know why exactly but I feel like you should only be able to offer a draw or resign only when it's your turn. After all resigning or offering a draw is a one-side choice, so maybe should count like a move in a turn.

You can resign whenever you like, I think though to offer a draw you need it to be your turn to be playing by the book, but I could be wrong.

You can resign no matter whose move it is-the proper draw etiquette is to make you move, offer the draw and the hit the clock.

You can resign any time of course.  But you should only offer a draw when completing your move as aansel decribed. You could offer a draw later while it's your opponent's move but don't do it repeatedly as they can object that you are trying to distract them.  You should not offer during your own time before your move, although if you offered a draw to me like that I might say "I'll think about it" and proceed to let your clock run down for a bit first...

But the act of offering draw or resignation is part of "your move", it's just a matter of style which comes first (the actual move and the words spoken).

Actually I believe if you offer a draw while it is your move, your opponent has the right to see what you move is and THEN decide if he wants to take the draw or not--so he has a nice option.