It is court ordered that my ex claim our son every other year so long as he is up to date on his child support. He is very far behind. What will happen if he does claim?

[Critter]

For him to claim the child as the non-custodial parent he must have a signed form 8332 from you ... without it the IRS will deny his claim.  

If someone else claimed your child inappropriately, and if they file first, your return will be rejected if e-filed. You would then need to file a return on paper, claiming the child as appropriate. The IRS will process your return and send you your refund, in the normal time. Shortly (up to a year) thereafter, you'll receive a letter from the IRS, stating that your child was claimed on another return. It will tell you that if you made a mistake to file an amended return and if you didn't make a mistake to do nothing. The other party will get the same letter you did. If one of you doesn't file an amended return, unclaiming the child, the next letter, from the IRS, will require you to provide proof. Be sure to reply in a timely manner.

Winner gets the tax benefits; loser gets to pay the IRS back with penalties and interest.  The custodial parent almost always wins.

IRS rules : 

The parent with whom the child lives more than half the year (184 or more 184 nights for 2016) is automatically entitled to claim the child as a dependent. This is the custodial parent. (IRS determines custody based on where the child lives, not any court order or agreement.)  The non-custodial parent is not entitled to claim anything.

However, the custodial parent can sign a release (form 8332) allowing the non-custodial parent to claim the child as a dependent.  You can download this form from the IRS web site.  The custodial parent signs it and gives it to the non-custodial parent and the non-custodial parent mails it to the IRS after e-filing the rest of their tax return.  In this case, the non-custodial parent can claim the dependent exemption and the child tax credit.  The non-custodial parent can never claim earned income credit, the dependent care credit (day care credit) or use the child to qualify for head of household status.  Those benefits always stay with the custodial parent.

[macuser_22]

Be careful with the 8332 form though.   There are 3 parts to the form.  Part I releases the exemption one time for the current tax year, however if part II was filled out on a prior 8332 form then the release is also for specified future years so a new 8332 form might not be needed if part II was filled out.

Part III revokes the future part II but does not take place until the year *after* part III is filled out.

It is best to never use anything other than part I or you might not be able to meet the requirements to revoke.  If the ex has a 8332 form with part II filled out, he might not need a new 8332 form in order to claim.

From 8332 instructions:
The revocation will be effective no
earlier than the tax year following the year
you provide the noncustodial parent with
a copy of the revocation or make a
reasonable effort to provide the
noncustodial parent with a copy of the
revocation. Also, you must attach a copy
of the revocation to your tax return for
each year you are claiming the exemption
as a result of the revocation. You must
also keep for your records a copy of the
revocation and evidence of delivery of the
notice to the noncustodial parent, or of
reasonable efforts to provide actual
notice.