Q: if you are a non-citizen woman and marry a citizen man. what about the children ?
A: Unless Kuwaiti law precludes dual citizenship, my understanding is that your children would be dual citizens (American and Kuwaiti), although depending on where you are living you may have to apply through the appropriate consulate to ensure that your children are citizens of whichever country you're not living in (ie if you're living in Kuwait, you would need to speak with the American consulate thereand vice versa). The very best advice I can give you is to consult an immigration lawyer. Perhaps someone at the consulate can recommend a lawyer. Good luck!