Polygamy, puh LIHG uh mee, can refer either to a system in which a man is married to more than one woman at the same time, or, less commonly, in which a woman is married to more than one man at the same time. The word polygamy comes from two Greek words meaning many marriages. Polygyny is a more specific term for the practice of marrying more than one wife. Polyandry refers to marrying more than one husband.