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.
Relinquishment of United States nationality
People who relinquish U.S. citizenship generally have lived abroad for many years, and nearly all of them are citizens of another country. Unlike most other countries, the U.S. does not prohibit its citizens from making themselves stateless, but the State Department strongly recommends against it, and very few choose to do so. It is usually impossible to relinquish citizenship while in U.S. territory, and courts have rejected arguments that U.S. state citizenship or Puerto Rican citizenship give an ex-U.S. citizen the right to enter or reside in the U.S. without the permission of the U.S. government. Like any other foreigner or stateless person, an ex-U.S. citizen requires permission from the U.S. government, such as a U.S. visa or visa waiver, in order to visit the United States.