My3 kids (15, 12 &7)live with my ex in Africa. Although they have never been in America before, a sizeable part of my income is remitted to them for their upkeep. Can I claim them when I file my taxes?

I've moved your post to the Tax forum. One of our tax experts will come along soon to answer. But I'm wondering if you could explain something to me. When you chose to ask a question in the Forum Help board, there was a bold red warning to read before posting. May I ask why you ignored that and didn't read the instructions for use of that forum?

This is a serious question as I'm trying to figure out a better way of directing people on the proper use of this site.

No, only the custodial parent has right to claim the chid. You are non-custodial parent and can claim the child only if
(a) The custodial parent signs a statement to allow you to claim the children, or
(b) There is a court order.

So may be you should talk to your ex. And if the children don't have SSN, attach W7 forms with your tax return.

Sorry, even with the divorce decree, your children CANNOT be claimed by you because they are NOT U.S. resident or U.S. citizen or U.S. nationals.

The ONLY exception to this rule is if you file jointly with your wife and BOTH of your world-wide incomes are subject to U.S. taxation. Under those circumstances, the children CAN be claimed as dependents.

Currently, you do NOT meet any of the criteria to be able to claim your children as dependents. Sorry!