Many traditional cultures including those in Yemen, Kenya, West Africa, South Africa and some parts of Asia engage in the practice known as polygamy which is an historical custom or religious practice of having more than one wife or husband at the same time. Though bigamy and polygamy are often confused bigamy is distinguishable from polygamy in that bigamy is a criminal act of marrying while the spouse of an earlier marriage is still alive and the former marriage is still in force. Bigamy is usually accompanied by a willful failure to inform the other spouse or the authorities. In immigration law the term bigamy and polygamy are distinct.
Before the Immigration Act of 1990 came into force, immigration law prevented foreign nationals from immigrating to the United States if the foreign nationals were polygamists, practiced polygamy or advocated the practice of polygamy .
Under the current law (Section 212 (a)(10)(10) of the Immigration and Nationality Act) a foreign national must actually intend to practice polygamy in the United States to be ineligible for an immigrant visa. The current law does not prevent a polygamist or someone who practiced polygamy in the past or expresses a belief in polygamy from being eligible for an immigrant visa. But aliens coming to the United States to practice polygamy are barred.
Even though a polygamous marriage is not recognized for issuance of an immigrant visa, the first that marriage that has not ended in divorce is not considered a polygamous marriage. For example if Poly Manner marriages wives #1, #2 and #3 in that order and remained married to them at the same time, the marriage to wife #1 is not considered a polygamous marriage and may be used to support an immigration petition.
A complication may arise however in obtaining an immigrant visa if a person is asked questions about multiple wives and admits to purposefully marrying more than one wife at the same time based on historical custom or religious practice . Such a person may be inadmissible under Section 212(a)(2)(A)(i)(I) of the Immigration and Nationality Act for admitting bigamy, a crime of moral turpitude  or for admitting acts which constitute the essential elements of bigamy.
But having more than one wife or husband without the benefit of divorce (e.g. the other spouse is believed to be dead, or her/his whereabouts are unknown) does not necessarily constitute a criminal offense  nor make a person ineligible for an immigrant visa.
 H.R. 10384, 64th Cong.
 See, Matter of G – 6 I & N Dec. 9 (BIA 1953)
 Braun v. INS, 992 F.2d 1016, 1017 (9th Cir. 1993)
 Example, Fla. Stat. §§ 826.01, 826.02 (2012)