Kleege grew up in La Jolla, California, but was born in Frankfurt, West Germany.

[3] Most of his singles matches in 1978 came in ATP Challenger events, but he made the main draw of the end of year Australian Open, in which he lost in the first round to Arthur Ashe, who was making his last appearance at the tournament.

[3] He started 1979 by winning the doubles title at the Lagos Open, a Grand Prix tournament, with Joel Bailey.

[7] He suffered the disappointment of losing a five-and-a-half-hour match in the final round of qualifying for the 1983 Wimbledon Championships, to Tian Viljoen, 11–13 in the fifth set.

[8] Later in the year he had an upset win over world number 14 and top seed Steve Denton at the 1983 Hall of Fame Tennis Championships in Newport.