Steevens made even as a young amateur attention to himself when he was touring with 19 years third in the Dutch stage race Olympia's. At the Olympic Games in Tokyo in 1964, he was part of the Dutch national team and has been used in cycling competitions in the Single Race Street. As the youngest of four Dutch starter he reached the 40th place among 107 evaluated drivers. 1965 won the 1.78 m wide Steevens in five races, including was again the Olympia's Tour, as well as the one-day race around South Holland. He also participated in the Tour de l' Avenir, in which he finished in sixth place in the overall standings. At the Tour de l' Avenir in 1966 Steevens was also at the start and came in the final accounts to the second place. For both trips, he was awarded as the best sprinter. First prize at the 1966 Ronde van Limburg -day race was Steevens 's last victory in a major amateur races.
In the fall of 1966, wrote Steevens 21 -year-old a professional contract with the Dutch cycling team Caballero and celebrated his first victory as a professional driver with a criterion in Ossendrecht. In addition to several victories in criteria and Kirmisrennen Steevens 1967 reached a third place in the Dutch -day race Amstel Gold Race. In the same year he made his debut as a professional road world championships with No. 17 In the two following years, he took up at the World Championships, but had the positions 18 and 25 is also little success. In Andalusia Tour 1968 Steevens won a stage though, came in the final score but only in 20th place His only significant victory in the 1968 season, he scored at the Amstel Gold Race. In 1969, he won again only in insignificant events. In addition to the World Cup, he also disappointing in such important races like the Amstel Gold Race ( 23 ), Paris -Tours ( 29 ) and the Tour of Lombardy ( 31 ). 1970 Steevens involved in the two stage race Tour de Suisse and Tour de France. In Switzerland, he won a stage and finished 24th in France, he was 45th among 100 evaluated assets. Also in 1971, now with the Dutch team Goudsmit under contract, he went back in two races at the start and was this time at the Tour de Suisse 44th in the Tour de France he got out prematurely. Although he went even 1972 Goudsmit, no results have been published for him.