the state, practice, or custom of being married to one person, or having only one sexual partner, at a time
Bigamy is having one husband too many. Monogamy is the same — anonymous, quoted by Erica Jong
in zoology, the habit of having only one mate
monogamist noun
monogamous /-məs/ adj
monogamously /-məsli/ adv
[French monogamie via late Latin from Greek monogamia from monogamos monogamous, from mono- + gamos marriage]