Damjanović represented Yugoslavia at first reserve board (+6 -2 =2) in the 14th Chess Olympiad at Leipzig 1960, and won individual silver and team bronze medals there. There was a second, more modest appearance for the national team at the European Team Championship, held in Hamburg 1965. His score of +1 -2 =6 was however good enough to contribute to a team silver medal. He was awarded the International Master title in 1962, and the Grandmaster title in 1964.