After Las Palmas returned to La Liga at the end of the 1963–64 season, again as champions, the club went on to have their most successful spell in the competition. Managed by Vicente Dauder, they finished third in 1967–68 behind Real Madrid and FC Barcelona, and four club players made the Spain squad which hosted and won the UEFA Euro 1964 tournament; the following season the team fared even better and only lost the league to Real Madrid, and thus qualified for European competition for the first time in its history, appearing in the 1969–70 Inter-Cities Fairs Cup and being knocked out in the first round by Germany's Hertha BSC (0–0 home draw, 0–1 away loss).