Stefan's father was a successful touring car racer and he started racing karts in Sweden in 1968. He won the Swedish title in 1973 and bought an old Formula Ford in 1975. He won the Swedish title in 1977 and in 1979 moved to Britain to contest the F3 championship. He won one race at Silverstone and was offered an F1 drive with Shadow for 1980. After two failures to qualify the Shadows, he concentrated on F3, winning the British title with six wins. In 1981 he moved into F2 with Toleman. He won at Hockenheim and Mantorp and was hired for 1982 by Spirit-Honda. It was a bad year with no victories but he tested the Spirit-Honda F1 car. He made his GP debut at the 1983 British GP. In 1984 he played the role as stand-in and raced with both Tyrrell and Toleman, finishing fourth in Italy for Toleman. He also competed in Japan, finishing second in the Japanese F2 series. He also won the Sebring 12 Hour IMSA race. He signed for Toleman for 1985 but it folded and was left driving a one-off race for Tyrrell in Brazil. Then Ferrari fired Rene Arnoux and Stefan stepped in. He scored two second places in Canada and Detroit and was seventh in the World Championship. This earned him a new Ferrari contract for 1986, but he switched to the McLaren-TAG team in 1987, finishing second in the Belgian Grand Prix behind teammate Alain Prost.