The high point of Klaus Kobusch’s career was probably at the 1964 Olympics, where in the tandem semifinals he and Willi Fuggerer apparently won 2-1 against the Italian team, but were disqualified in the third race for moving out of their lane in the sprint. Fuggerer and Kobusch protested without success and won bronze after beating the Dutch team in the third-place race. Kobusch came back at Mexico City in 1968, by then representing West Germany, together with Martin Stenzel, but the tandem was eliminated in the quarter-finals. Both earlier earned a silver at the 1966 Worlds.
Kobusch was awarded the Silver Bay Leaf in 1964, the highest sports award in Germany. He won 10 West German titles from 1964-68. In 1969 Kobusch retired and worked as a cycling coach, but he later became an insurance agent.