monogamous
adjective
mo·nog·a·mous mə-ˈnä-gə-məs 
variants or less commonly monogamic
ˌmä-nə-ˈga-mik
: relating to, characterized by, or practicing monogamy : having only one mate, spouse, or sexual partner at one time
… the beaver has several qualities that endear it to people: it is monogamous and lives in a family unit; it is gentle and clean; it is absolutely industrious.
Doug Hand
Doug HandBut for women who are not at risk for STDs because they are in mutually monogamous relationships, modern IUDs can be safe and very effective. Kim Painter
Kim PainterThere are many kinds of infidelity, but here we are talking about a sexual infidelity in monogamous marriage or a relationship that is tantamount to marriage. Frank Pittman
Frank Pittman monogamously adverb
Pairs usually mate monogamously for life … Vincenzo Penteriani et al.
Vincenzo Penteriani et al. 
Did you know?
What is the Difference Between monogamous and Polygamous?
American marriage is by law monogamous; people are permitted to have only one spouse at a time. There are cultures with laws that permit marriage to more than one person at a time, or polygamy. Although the term polygamy may refer to polyandry (marriage to more than one man), it is more often used as a synonym for polygyny (marriage to more than one woman), which appears to have once been common in most of the world and is still found widely in some cultures.
Word History
First Known Use
1770, in the meaning defined above