In the 1982–84 World Chess Championship cycle, he qualified for the Candidates Tournament, losing to eventual winner Garry Kasparov in the quarterfinals of the 1983 Candidates matches. Beliavsky played on the top board for the USSR team that won the gold medal in the 1984 Chess Olympiad. Beliavsky was a mainstay at international tournaments throughout the eighties and early nineties, however, he did not perform to the highest levels. In the 1985-87 Candidates he finished 7/16, but neither qualified for the 1988-90 Candidates tournament nor the 1994-95 PCA Candidates tournament.