Claiming children after divorce

I live in Wash. state and our final divorce papers state that I claim the children for tax purposes. I received a letter from the I.R.S. today saying that I was one of two people to claim the given S.S. #'s(children). The other must have been my ex. I was told that I didn't need to do anything because I have court ordered rights to claim them. Will my ex have to pay back the money he received, and would it be fair to let him have one exemption even though I make less and pay all out of pocket expenses?

If I were you I would respond to the IRS with a photocopy and a letter of the divorce decree. This will certify to them that he is in fact responsible for paying them.

As for fairness, I would say (excuse my loud opinion) that there was a reason that you got to claim them for tax purposes. He has already tried and failed to claim them while you are. I would doubt that this was a mistake. Yes, you can alternate who claims them, but don't let him walk all over you. And don't change any of that legally because then you hold the trump card if he fouls up another agreement about taxes.