Adolff had enjoyed competition on home soil driving Mercedes 170 saloons along with Fritz Riess and Karl Kling. But his performances with the 2-litre Veritas RS sports between 1950 and 1952 brought him to the fore, his results including two third places at the Nurburgring.
In 1953 Kurt joined Ecurie Espadon, handling Swiss driver Rudi Fischer's Ferrari. After bringing it into a distant fourth place in the Eifelrennen, he retired the same car in that year's Grand Prix.
Adolff subsequently competed in hill-climbs with a Jaguar.