In the United States, individuals may only be married to one person. Polygamy is illegal and individuals may be prosecuted, even when it is practiced in their religion. In fact, individuals that immigrate to the United States may only declare one spouse upon entering the country, even if they are legally married to several people in their country of citizenship.
Individuals that have already been married must be legally divorced before they may again marry. A legal separation does not qualify and individuals are breaking the law if they get married before a divorce is finalized.
In fact, those that are illegally married are not subject to the rules of divorce if they should separate or become divorced. For example, spouses may not collect spousal support payments. However, if one spouse was unaware that the marriage was not legal, the judge may award payments because of the act of fraud.
