You are an American citizen unless you have renounced it. If you are naturalized, the oath requires you to renounce other citizenship. Now, the second country might consider you to maintain dual loyalties. The U.S.A. does not.
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(This argument has really become more than just crushingly boring to the rest of us with duals. Read up!)
“But I thought US law didn’t permit one to be a dual citizen — that if you were (by birth or otherwise), you either had to give up the other citizenship when you came of age, or else you’d lose your US status. And that if you became a citizen of another country, you’d automatically lose your US citizenship. So what’s all this talk about dual citizenship?”
“It indeed used to be the case in the US that you couldn’t hold dual citizenship (except in certain cases if you had dual citizenship from birth or childhood, in which case some Supreme Court rulings — Perkins v. Elg (1939), Mandoli v. Acheson (1952), and Kawakita v. U.S. (1952) — permitted you to keep both). However, most of the laws forbidding dual citizenship were struck down by the US Supreme Court in two cases: a 1967 decision, Afroyim v. Rusk, as well as a second ruling in 1980, Vance v. Terrazas.”
“Rules against dual citizenship still apply to some extent — at least in theory — to people who wish to become US citizens via naturalization. The Supreme Court chose to leave in place the requirement that new citizens must renounce their old citizenship during US naturalization. However, in practice, the State Department is no longer doing anything in the vast majority of situations where a new citizen’s “old country” refuses to recognize the US renunciation and continues to consider the person’s original citizenship to be in effect.”
“The official US State Department policy on dual citizenship today is that the United States does not favor it as a matter of policy because of various problems they feel it may cause, but the existence of dual citizenship is recognized (i.e., accepted) as a fact of life. That is, if you ask them if you ought to become a dual citizen, they will recommend against doing it; but if you tell them you are a dual citizen, they’ll almost always say it’s OK.”