Monogamous

adj. of monogamy, of marriage to one person at a time

Monogamy is the custom or condition of having only one mate in a relationship, thus forming a couple. The word monogamy comes from the Greek word monos, which means one or alone, and the Greek word gamos, which means marriage or union. Serial monogamy is having no more than one sexual partner at a time but allows for multiple partners in a lifetime. In western culture serial monogamy is common with individuals before they start a family, due to divorce rates. The opposite of monogamy is polygamy.
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Mo·nog·a·my n. 1. The practice or condition of being married to only one person at a time. 2. The condition of having only one mate. [more]Monogamous - Community and Resources

Adjective
1. (used of relationships and of individuals) having one mate; "monogamous marriage"; "monogamous for life"
(antonym) polygamous
(similar) monandrous

(a.)
Upholding, or practicing, monogamy.
  

(a.)
Same as Monogamian.
  

(a.)
Mating with but one of the opposite sex; -- said of birds and mammals.