Koevermans became a professional tennis player in 1987, and the following year he won his first tournament victory in singles on the ATP Challenger Tour . He also won the double competitions of the Challenger tournaments in Travemünde and Tampere on the side of Igor Flego . In 1989 he was in the finals of the Challenger tournaments in Agadir and Casablanca , in the latter he won the doubles competition together with Josef Čihák . In 1990 he celebrated his only individual title on the ATP World Tour in Athens , and he was also three times in an ATP double-final. The following year he won his first double title on the ATP Tour alongside Jacco Eltingh in Athens ; He won another title with Paul Haarhuis , with whom he played frequently and very successfully. Together they won three tournaments, including the Masters tournament in Hamburg , and were in the finals of seven other tournaments, including twice at the Masters tournament in Monte Carlo . Overall, Koevermans won four double titles in his career, twelve more times he was in a double final. He achieved his highest scores in the ATP world rankings in 1991 with position 37 in singles and in 1993 with position 24 in doubles.
His best individual result in a Grand Slam tournament was the entry into the round of 16 at Wimbledon in 1990, his best result in the doubles competition was the semi-finals at the French Open in the same year.
Koevermans played nine singles and six doubles games for the Dutch Davis Cup team between 1988 and 1993 . His greatest success with the team was a quarterfinal participation in 1993 (world group) against Sweden ; he lost the double at Paul Haarhuis's side. At the 1992 Olympic Games in Barcelona he competed in singles and doubles for the Netherlands. With Paul Haarhuis he had to admit defeat in the first round to the later bronze medalists from Croatia , Goran Ivanišević and Goran Prpić . In singles he reached the third round, in which he was defeated by Jaime Oncins .