Unlike the Romulan Neutral Zone, the Organian Neutral Zone appears to have been set up during the time of the Star Trek: The Original Series. Also unlike the Romulan Neutral Zone, the Organian Neutral Zone appears to have some commercial traffic crossing it.
The zone was the site of the Kobayashi Maru scenario. The Organians are non-corporeal beings from the planet Organia IV, which is strategically situated between the Empire and the Federation. When both parties, thinking them a pre-industrial people, attempted to occupy their world, the revealed their posthuman nature and imposed the Neutral Zone.