In 1979, Thurau won Liège–Bastogne–Liège, and again came second in the 1979 UCI Road World Championships, but he was no longer seen as able to win a grand tour, and he changed teams. He continued as a professional cyclist for several years, but did not win any major races. Thurau tested positive for stimulants after Stage 8 of the 1987 Tour de France. He was fined 5,000 FF (£500), incurred a 10-minute time penalty, placed last on the stage and was given a one-month suspended ban. However, by the time the positive result was revealed, Thurau had already abandoned the Tour. After he had retired, in 1989, he gave an interview to the Bild newspaper, in Germany, where he revealed he had doped throughout his career, including the use of Amphetamines, Testosterone and Cortisone. In 1998, Thurau was fined 20,000 DM for forgery. In 2012, it was reported that he had embezzled 49,000 EUR in insurance benefits, which were meant for his father, Helmut, to pay for his nursing home. Instead, Thurau kept the money. He was convicted of the offence and was fined 39,900 EUR. His son Björn Thurau is also a racing cyclist, whilst Björn's younger brother Urs is a tennis player who is coached by Dietrich.