Team Logo. The Dallas Tornado was a team in the North American Soccer League (1968-1984). They played the longest of the league's original teams. They folded in 1981. Retrieved from "https://prosportsteams.fandom.com/wiki/Dallas_Tornado?oldid=11660" Categories: NASL (1968-1984) Teams Teams in Texas Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.