Zeman achieved his first international successes at the Junior European Championships: in 1974 he finished third in giant slalom and in 1975 second in slalom. Zeman won his first points in the World Cup on January 9, 1976, with 7th place in the Kandahar combination of Garmisch-Partenkirchen . In the same year he took part in the Olympic Winter Games in Innsbruck . In the 1976/77 season he could only classify in the points once, not at all the following winter. He achieved consistently consistent performances in the 1978/79 season, with a total of five placements among the top ten.
Zeman was similarly successful in the winter of 1979/80 with five other top 10 placements. At the 1980 Winter Olympics in Lake Placid , he finished fourth in the combined ranking, which only counted as a world championship. On March 1, 1980, he went on the podium for the only time in a World Cup race, when he came third in the giant slalom of Mont Sainte-Anne behind Ingemar Stenmark and Phil Mahre . In the winter of 1980/81, fourth place was Zeman's only classification in the World Cup. On the other hand, he won the Hahnenkamm combination from Kitzbühel , which was not part of the World Cup that season. At the end of the 1981/82 season he resigned from top-class sport.
Czechoslovakia
