When he was 11 he had his first experience with motorcycles on the DKW RT 125, but soon afterwards he chose skibobbing as his favored sport. He was successful at this sport, winning the German National Championship as well as the Junior European Championship in skibobbing at the age of 16.

Still, motorsports kept pulling at him and he took part in a 50cc race on a Kreidler two years later though he had to pull out of the race due to mechanical difficulties.

In 1970 Mang joined the reigning 125cc world champion Dieter Braun's team as his mechanic. Together with Sepp Schloegl and Alfons Zender Mang, he developed the "Schloegl Mang Zender" (SMZ 250). With this machine, he took part in a race on an airfield in Augsburg and claimed his first victory. In 1975 he won the German Championship on 350cc Yamaha. Also in 1975 he competed in his first Grand Prix at the Austrian round of the world championship.

His first Grand Prix victory came at the 1976 German Grand Prix at the 22.8 km Nordschleife Circuit at Nürburgring on a 125cc Morbidelli. His success earned him a ride with Kawasaki for the 1978 season in the 250cc and 350cc classes. In 1980 he became World Champion in the 250 cc class and runner-up in the 350cc class behind Jon Ekerold. In 1981 he won both the 250cc and 350cc World Championships and became German Sportsman of the Year. In 1982, he became the last ever 350cc World Champion as the class was abolished at the end of the year. He fell just one point short of defending his 250cc championship, despite winning five races.

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Wikipedia