I just got a Swedish passport for my son, born here in USA.
He is now dual, but we live in the States. His dad is American and
I'm Swedish (his mother).
My question is, does he need an American as well for travelling,
Or is the Swedish one enough?
Our daughter has both and has been to Sweden a few times. I can't
Remember if the Swedish one would have been enough for her coming
Back to the country.
Hope for answer.
Many thanks,
Jill

From what I have been told, your kids would need an American pasport to get back into the USA.

Something about the laws requiring that all American citizens use American passports in America.

I think the answer from CaptainForest is right, your son needs a US passport to re-enter the US. But even if he doesn't need one, he should have one to avoid all kinds of red tape and paperwork when re-entering the US.