Mronz 'highest ranking on the tennis world rankings was in singles place 73 in 1991. In singles he won no tournament, in doubles, however, he managed a tournament victory. He had his greatest single success in 1995 at a Grand Slam tournament at Wimbledon. His third-round opponent, the American Jeff Tarango , lost his composure after the French referee Bruno Rebeuh had deducted points , accused Rebeuh of corruption and left the pitch. The match was canceled and Mronz declared the winner. This entry into the round of 16 at Wimbledon was the furthest advance by Mronz as a single player in a Grand Slam tournament.