Beresch's breakout year was 2000; in this year he was the European all-around and high bar champion, as well as the bronze all-around medalist at the 2000 Olympics. His contributions to the Ukrainian team helped them win their first team medal, a silver, in Sydney. He continued to turn in strong performances after the Olympics, winning three medals at the 2001 World Artistic Gymnastics Championships and winning the high bar gold at the 2000 World finals in Paris.