po·lyg·a·my 
(pə-lĭgə-mē)
(pə-lĭgə-mē)n.
1. The condition or practice of having more than one spouse at one time.
2. Zoology A mating pattern in which a single individual mates with more than one individual of the opposite sex.
[French polygamie, from Late Latin polygamia, from Greek polugamiā : polu-, poly- + -gamiā, -gamy.]