Nordmark was drafted 191st overall in the 1981 NHL Entry Draft by the Detroit Red Wings, after helping Sweden to their first gold medal at the World Junior Championships in 1981. Despite solid performances in the Swedish Elite League in ensuing years, Nordmark was never signed by the Red Wings and his draft rights lapsed in 1984. After strong performances at the 1986 and 1987 World Championships, Nordmark was re-drafted 59th overall in the 1987 NHL Entry Draft by the St. Louis Blues.