Team Logo. The New York Cosmos, not to be confused with the current Cosmos, was a team in the North American Soccer League (1968-1984). They won the Soccer Bowl 5 times, the most of any team. They folded in 1984. Retrieved from "https://prosportsteams.fandom.com/wiki/New_York_Cosmos_(1971-1984)?oldid=11603" Categories: NASL (1968-1984) Teams Teams in New York Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.