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.
Dual intent
Certain types of foreign visitors are allowed dual intent, and other categories of visitors are not. Persons with H-1B visas (for specialty workers and their spouses and minor children with H-4 visas), K visas (for fiancees or foreign spouses of US citizens and their minor children), L visas (for corporate transferees & their spouses and minor children), and V visas (spouses and minor children of lawful permanent residents) are permitted to have dual intent under the Immigration and Nationality Act. Federal regulations also appear to recognize dual intent O visas (for workers who have extraordinary ability and their spouses and minor children), P visas (for athletes, artists or entertainers and their spouses and minor children), and E visas (for treaty traders or treaty investors and their spouses and minor children).