Nataliya Glebova made her international début at the 1982 European All-around Championships where she won a bronze medal in all-around and silver in the 500 and bronzes at 1,000 and 1,500. In 1983, Glebova won silver and gold in the 500 at the European and World All-around Championships, respectively, but a poor performance in longer distances denied her a higher place than eighth in both of those championships. At the 1984 World All-around Championships Glebova again won silver at 500 m, while at the 1984 Olympics she won bronze in the 500. After the Olympics, Glebova won bronze at the World Sprint Championships and continued to skate a few more seasons, but with less success, finishing her skating career after competing at the 1988 Olympics. Domestically Glebova won Soviet titles in the all-around in 1983, in the sprint all-around in 1984, the 1,000 m in 1982 and 1984, the 3,000 m in 1983, and at 5,000 metres in 1983.
Personal Bests: 500 – 40.39 (1983); 1000 – 1:22.22 (1984); 1500 – 2:09.36 (1982); 3000 – 4:37.97 (1983); 5000 – 8:07.20 (1983).