His biggest success was the bronze medal in the 5,000 meter run at the 1988 Summer Olympics in Seoul, Korea.

He had a spectacular win on 9 September 1981 in Rieti, Italy, when he set a European record in the 5,000 meter run with a time of 13:10.40 and beat Kenyan Henry Rono who had dominated that season.

Also Wolfgang Wünsche's class book about athletics, "The Heroes of Race Tracks," in its 1984 edition (translated into Finnish), includes references to Kunze's bronze medal in the 1983 World Championships, his decision not to run the 5,000 metres in those championships, his failure at 5,000 metres in the 1982 European Championships (he finished ninth after being pushed around in the crowded group of runners – see, for example, a Finnish book called "Highlights of Top Sports" / Huippu-urheilun tähtihetkiä), and his success at 5,000 metres in the 1981 European Athletics Cup.

Since the end of his sport career he has worked as a journalist for a public relations agent for an athletic shoe manufacturer, as commentator for the 1993 World athletic championship in Stuttgart, as a radio and television reporter for a regional station and lastly as a spokesperson for a shipping company.

In 2004 he worked for the Rostock Olympic bid committee (for the sailing competition that would be held in Leipzig).