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monogamous (adj.)

of humans, "having or permitted to have but one living and undivorced wife or husband at a time," 1778 (of animal pairings from 1770), from Medieval Latin monogamus, from Greek monogamos "marrying only once" (see monogamy). Also sometimes "not remarrying after the death of a spouse." Related: Monogamist (1650s); monogamistic.

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Definitions of monogamous from WordNet

monogamous (adj.)
(used of relationships and of individuals) having one mate;
monogamous for life
monogamous marriage
From wordnet.princeton.edu