Alex was born on July 5, 1968 in Wil, Kanton St.Gallen, as the first child of Walter and Wilhelmine Zülle. His mother comes from Brabant, the Netherlands, but Alex grew up in Switzerland. Two years later, the family grew to include his sister Claudia. According to his mother, little Alex's favorite pasttime was playing Cowboys and Indians in the woods with his friends.

Alex is very fond of children. He gave his leader's and points' trikots from the 2002 Tour de Suisse to his sister's children, and finds it hard to say no to his many little fans. When his career is over he would like to start a family, but doesn't feel he has the time for it now. Marriage to his girl-friend Andrea is also waiting until the end of his career, although they have been together since New Years Eve 1992. A dream came true for him with the construction of his own house in the small town of Zuckenreit (pop. 650) between Wil and St. Gallen. There he can relax during in his off-time, for example in his private sauna. According to Andrea, Alex is very finicky and pitches in to help keep the house clean and in order.In his limited free time he enjoys swimming, going out and going on vacation. He describes himself as a "pleasure-lover," and according to his countryman and friend Ralf Järmann, is crazy over potato chips and chocolate.