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."