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1.
The grey area in between taking the plunge into a committed relationship and platonic friendship. Often due to indecision on the part of one or more parties involved.

Symptoms might include, holding hands, non-committal sex, spending an inordinate amount of time together, flirting on text messages.
"Sam and Jane have been having this non-relationship for months now, they need to decide whether or not they are going out or not."
by atreidai July 25, 2005
 
2.
A situation of unusual tension where two people are fooling around but are unwilling to give their interactions a name. There are no expectations and no ground rules, and no one knows where they stand, but it's a safe bet that they're textually active and they probably see each other twice every three weeks and have pretty hot hookups.

When something's going on, but it's not dating, and it's not a booty call, it's not a serious relationship, it's not hooking up, and it's not friends with benefits... what you've got on your hands is a nonrelationship.
Chick1: Paul texted me Thursday to party at his place Saturday night. I think I'll spend the night.
Chick2: Cool, so you're into him?
Chick1: Yeah, kinda.
Chick2: Is it going anywhere?
Chick1: Not really, but I want to consummate our nonrelationship.
by mayasd November 04, 2008