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1. An exclusive and ostensibly romantic relationship that is devoid of sex. Typically, it is because one partner witholds due to emotional distance or other non-sexual reasons, but still expects the other to not stray.

2. A sarcastic reference to modern monogamy in the developed world where sex is marginalized or disappears in a marriage in favor of career, child rearing, bills, fatigue and other domestic issues.
When the subject of Paul's cheating came up at the marriage counselor, he sharply retorted "Denise had a 2 -year headache. She didn't want monogamy, she wanted nonogamy, and that's not what I signed up for when I married her."
by J Philip August 19, 2007
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2
The choice to remain single and unmarried by someone's own free will, and the unwillingness to enter a relationship.
Friend: Are you getting married?
Me: Nope, I'm going with nonogamy.
by wissMngm June 05, 2018
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