 The AFL merged with the NFL in 1970, and the Dolphins were assigned to the AFC East division in the NFL's new American Football Conference.For the rest of the 20th century, the Shula-led Dolphins emerged as one of the most dominant teams in the NFL with a strong running game and defense, with only two losing seasons between 1970 and 1999.They were extremely successful in the 1970s, completing the first complete perfect season in NFL history by finishing with a 14–0 regular season record in 1972 and winning the Super Bowl that year.