I lived in Canada (not overseas, but...) and filed a form each year saying, essentially, that I had paid my taxes in Canada and had lived and worked in that country for the entire tax year.

I forget the form number now, though. The form was the same for the years when I was in Canada part time and in the US part time - I just had to file / pay taxes for that time during each of those years when I was living in / operating in the US.