Children don't have ssn, can I still file taxes?

You cannot claim the child as a dependent on your tax return if they do not have a Social Security number or an ITIN issued to them by the IRS.

What is the situation on why they do not SS numbers or an ITIN?

If your children do not have SSN's then you cannot include them on your tax return.  If you plan to get them SSN's then you can file an extension so they have one by the time you file.   

Why don't they have them?  Are they US residents?  Born late last year?