The trained police officer Kunc won his first points in the World Cup at the giant slalom in Veysonnaz in January 1990 . His breakthrough to the top of the world came in the mid-1990s when he achieved a few second places in the giant slalom. In 1994 he finished fourth at the Olympic Winter Games in Lillehammer , just nine hundredths of a second behind his teammate Jure Košir . He finished seventh in the combination .
His athletic development was then stopped by injuries. Only at the end of the 1990s was he able to build on his earlier successes as a slalom runner. On 27 February 2000, he won the slalom of Yongpyong the only World Cup race of his career. At the 2001 World Ski Championships in St. Anton , he won the bronze medal in slalom. During the 2001/02 season some top placements followed. But then he was stopped again by injuries.
Kunc ended his active career on February 27, 2005. In the slalom in Kranjska Gora , he started as a forerunner. In the middle of the run he stopped and said goodbye to his trainer Janez Šmitek . Before the finish line he stopped a second time and his teammates carried him into the finish area.