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.
Austrian nationality law
An Austrian citizen who acquires another citizenship by voluntary action automatically loses Austrian citizenship. The exception is in cases where permission to retain Austrian citizenship has been obtained in advance. This may be difficult to obtain, as the aim of the lawgiver is to reduce the number of dual citizenships granted. Exceptions are made for situations where it is in the interest of the Republic of Austria to grant this dual citizenship (e.g. when somebody is a celebrity in arts, sports, science, economy etc.), or in situations where the citizen would suffer hardship due to not having the second citizenship. If, for example, an Austrian citizen wants to obtain U.S. citizenship because he/she lives in the U.S. and, without a U.S. citizenship, would lose their green card due to being made to travel more than 180 days per year by their employer, then if they apply for permission to retain Austrian citizenship, that request is usually granted and has become almost a formality.