While never an individual star, István Móna was on the strong Hungarian team that dominated modern pentathlon between 1963 and 1968. Móna and his team mates András Balczó and Ferenc Török won the World Championships four times in a row, 1963, and 1965-67, topping off their streak with an Olympic gold medal in Mexico. At the Hungarian Championships, Móna never won the individual title, finishing runner-up on three occasions (1963, 1966 and 1967), but he did win four team titles. In addition, Móna also won a Hungarian title in fencing, winning the épée team title in 1970. Móna remained involved with his favorite sports: he coached both sports at a club level, and worked with the national pentathlon team in the 1990s. He also served in the Hungarian fencing federation and the Hungarian NOC.