EZED, this is what we received from the IRS as of 2/20/08 (excerpted of course).
Only taxpayers who file a 2007 tax return with valid Social Security numbers will be able to receive a stimulus payment. If filing a joint return, both spouses must have valid Social Security numbers. And, children must have valid Social Security Numbers to be eligible as qualifying children. Individual taxpayer Identification Numbers (ITINS) and adoption taxpayer identification numbers (ATINs) are not eligible.
You can also find some information on the IRS website itself:
http://www.irs.gov/irs/article/0,,id=177937,00.html
So, if your children had at least $3000 of earned income, have a valid Social Security Number, and filed a return for 2007, they should be eligible for the rebate. The IRS makes mention of this, however, in the link above (emphasis added):
Q: I know some people won’t get a stimulus payment. How do I know if I’m one of them?
A: You won’t get a stimulus payment in 2008, if any of the following apply to you:
-You don’t file a 2007 tax return.
-Your net income tax liability is zero and your qualifying income is less than $3,000. To determine your qualifying income, add together your wages, net self-employment income, nontaxable combat pay, Social Security benefits, certain Railroad Retirement benefits and certain veterans’ payments.
-You can be claimed as a dependent on someone else’s return. For example, this would include a child or student who can be claimed on a parent’s return.
-You do not have a valid Social Security Number.
-You are a nonresident alien.
-You file Form 1040NR or Form 1040NR-EZ, Form 1040PR or Form 1040SS for 2007.
However, given your posted rudimentary scenario, it looks like you would not be claiming your children anyway. You probably want to figure your return and that of your children to see if your refund, if any, amounts to the rebate checks your children may be getting. In other words, do your return with you claiming them both, and then do their returns where they (1) claim themselves and (2) do not claim themselves. This is what we have to do all the time, especially with that doggone Hope Credit and Lifetime Learning Credit. Speaking of which, if you are paying their college tuition, you can claim this credit, depending on your AGI.
Clear as mud, eh? PM me if you have more questions and I'll ask the IRS specialist on staff.