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. law permits multiple citizenship. A citizen of another country naturalized as a U.S. citizen may retain their previous citizenship, though they must renounce allegiance to the other country. A U.S. citizen retains U.S. citizenship when becoming the citizen of another country, should that country's laws allow it. U.S. citizenship can be renounced by Americans who also hold another citizenship "via" a formal procedure at a U.S. Embassy, and it can also be restored.