Since July 1, 2001, Sweden allows dual citizenship. U.S. citizens residing in Sweden who are interested in applying for Swedish citizenship should be aware of the following guidance on U.S. nationality policy:
Information on dual nationality
Information on renunciation of U.S. citizenship
Read more about the U.S. standpoint on citizenship and nationality at the State Department website.
Entering and Departing the U.S.
According to Section 215 of the U.S. Immigration and Nationality Act (8 U.S.C. 1185), it is illegal for an American citizen to enter or leave the U.S. on anything other than an American passport. This applies to dual citizens as well, meaning that persons holding e.g. both Swedish and American citizenships and passports must enter and leave the U.S. on a U.S. passport. They may not enter/leave the U.S. on a Swedish passport. This applies to children as well as adults.