Claiming dependents in US

My ex wants whom lives in the USA wants to claim both our sons whom live with me in the UK on his tax return. Is this legal? I know he has been doing it for the past four years with my permission but he just asked me to renew the form to give him permission to claim them (cant remember the form number). Anyway he has a lot of nerve asking me for it in the first place but can he actually legally claim them if they are UK residents?

if he pays you money..and ACTUALLY supports  them  I would assume.. 

I'd say: I'll sign the tax form when you sign the passport forms. 

I thought it was more to do with who the children lived with. Since they live with you,, they would not really be his dependents?  I think you have been very generous to let him use them as a tax break.

My divorce decree specifies who gets to claim the kids as dependents for US taxes. 

My divorce decree specifies who gets to claim the kids as dependents for US taxes.

Yes, our decree states I will claim one child and he would claim the other however he is asking permission for himself to claim both children when Im not sure he is legally able to claim them anyway. I was looking at the IRS site and there are a few tests you can take. The kids are UK residents but US citizens so I think he is able to claim them however he sees them for a week a year and doesnt contribute to half their support.

I believe that until/unless your divorce decree is modified, he is still entitled to claim one as a dependent.  The form that you fill out (forget the form # as well) basically provides an exemption from them having to live with him.  However, it's my understanding that he could not claim either one of them for 'earned income credit' as I believe there is a residence requirement for that.  He's not legally entitled to claim both of them.  It's been nice of you to allow him to do so, but that's by your good graces.