Citizenship of the United States
A person who is considered a citizen by more than one nation has "dual citizenship". It is possible for a United States citizen to have dual citizenship; this can be achieved in various ways, such as by birth in the United States to a parent who is a citizen of a foreign country (or in certain circumstances the foreign nationality may be transmitted even by a grandparent) by birth in another country to a parent(s) who is/are a United States citizen/s, or by having parents who are citizens of different countries. Anyone who becomes a naturalized U.S. citizen is required to renounce any prior "allegiance" to other countries during the naturalization ceremony; however, this renunciation of allegiance renunciation of citizenship to those countries.
Citizenship of the United States
U.S. citizens are required by federal law to identify themselves with a U.S. passport, not with any other foreign passport, when entering or leaving the United States. The Supreme Court case of "Afroyim v. Rusk" declared that a U.S. citizen did not lose his citizenship by voting in an election in a foreign country, or by acquiring foreign citizenship, if they did not intend to lose U.S. citizenship. U.S. citizens who have dual citizenship do not lose their United States citizenship unless they renounce it officially.