I suggest you confer with an attorney who will want to review the exact wording and terms of the divorce decree and she/he can then assist you and advise you. You may view the irs.gov website. We avvo attorneys are available.
MINNEAPOLIS/ST. PAUL and outlying areas to ST CLOUD. Do seek legal counsel for your personal legal issues and needs. This post is not legal advice and does not create an attorney-client relationship. This post is to be considered general information which may or may not apply to your personal situation.
Under federal tax law, if they were in your physical custody more than they were in his physical custody for the tax year (2013) then you are entitled to claim all of the children as your dependent. This right under federal law can be awarded to the non-custodial parent in a divorce. The parents can also enter a contract to give the non-custodial parent the right. A verbal agreement usually is a contract if it is supported by consideration. I can't tell from the information that you have given whether your statement that he could claim 2 of the four children is a contract. (It probably should have been dealt with in the divorce). Even if your statement is a contract, an argument can be made that a condition of your promise was that he pay child support. I would talk to your divorce lawyer or a tax lawyer about how to proceed. It may be in your best interest to work out an agreement and split whatever reduction in taxes he might get by letting him take the two children. Or let him claim the two children if he catches up in child support. There are many avenues to work out an agreement.
If there is nothing in writing in the decree regarding the dependency exemption, the parent who had the child the majority of overnights for the year is entitled to it and does not have to give it up.
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If your Divorce Decree did not address the issue of claiming your children for tax purposes and you have primary physical custody (you have the children for 55% + of overnights) you do not have to let him claim them. However, this issue could be an on-going point of contention for the future. It might be best to meet with a lawyer who can help resolve the matter, both for this year and going forward.