Monogamy was the practice of having a single spouse, as opposed to multiple marital partners.
In 2365, Doctor Katherine Pulaski advised the Bringloidi and Mariposans to avoid monogamous marriage for several generations to create a broad genetic base in the interests of health and safety. (TNG: "Up The Long Ladder")
In 2375, the Silver Blood replica of Seven of Nine caught "B'Elanna Torres"'s bridal bouquet, signifying that she might be the next person to marry. When "Torres" suggested "Harry Kim", "Seven" replied that she didn't see any benefit in monogamous relationships. She further clarified that she wished not to be dependent on anyone, and found the prospect of being romantic with a single individual boring. (VOY: "Course: Oblivion")