On July 1, 2001, a new Citizenship Act came into effect in Sweden. The new law makes it possible to have dual citizenship.
The law also gives children further opportunity to become Swedish citizens independent of their parents.
If you are a Swedish citizen and become a citizen of a second country, the new law means that you can keep your Swedish citizenship if the other country permits it. By the same token, if you become a Swedish citizen you can keep your foreign citizenship if the laws of that country permit it.
The U.S. State Department requires that all U.S. citizens, including those who have dual citizenship, must be in possession of a valid U.S. passport when leaving and entering the U.S. It is thus advisable for dual citizens to bring both passports when traveling internationally.
A provisional regulation made it possible for those who had lost their Swedish citizenship as a result of being granted citizenship in another country before July 1, 2001, to regain their Swedish citizenship through notification before June 30, 2003. This retroactive provision is no longer in effect.
> Read more at the Swedish Migration Agency website