Monogamy or Monoamory is describes an exclusive relationship between exactly two people. Monogamous can be used both as a description of a relationship with exactly two people and as description of people who desire such relationships. Ideally, both participants in a monogamous relationship only have a single partner at a time, and it is not an open relationship. The term monogamous is commonly used by polyamorous people to describe relationships with only two people.
Monogamy vs. Monoamory
Under the most strict definition of the term, monogamy refers to being married to a single person at a time, while monoamory refers to being in a relationship with a single person at a time. However, the term monogamy has come to be used as in a more broad sense and can be used regardless of whether the people involved are married.