His highest placement on the tennis world ranking was number 73 in the single in 1991. In individual he could not win a tournament in a double on the other hand, he managed a tournament victory. He had in 1995 at a Grand Slam tournament at Wimbledon, his greatest single success. His third- round opponent, the American Jeff Tarango, lost by a point deduction by the French referee Bruno Rebeuh the wording Rebeuh accused of corruption and left emotionally charged the square. The match was canceled and Alexander Mronz declared the winner. This first knockout round of Wimbledon was the farthest advance of Mronz as a single player at a Grand Slam tournament. In November 1996 Mronz announced his career-ending.
Alexander Mronz is a son of the Cologne architect John Mronz. In 1989 he became the world mainly because known that he was the first friend, Steffi Graf presented in public. His brother Michael is a sports manager and the spouse of the politician Guido Westerwelle.