At the 1988 Olympics in Seoul, she won at the age of 14 years to compete over 200m backstroke. She was making her the youngest gold medalist in swimming at the Olympics at all, but was undercut by Kyoko Iwasaki 1992 by 32 days. They also won in 1988 the silver medal over 100 m backstroke. At the Olympic Games in Barcelona in 1992 she was awarded three gold medals (100 m backstroke, 200 m backstroke and 400 m IM ) is the most successful athlete in the women. By another gold medal at the 1996 Olympic Games in Atlanta in 200m backstroke she had succeeded, three times to win consecutively in the same discipline. Similar success in Olympic swimming competitions in the Single 've only the Australian Dawn Fraser (1956, 1960 and 1964 Olympic gold in the 100 m freestyle ) and the American Michael Phelps ( respectively 2004, 2008 and 2012 Olympic gold in the 100 m butterfly and exhibit 200m Individual Medley ). Egerszegi also won the bronze medal in Atlanta about 400 m medley.
Egerszegi improved in their careers the world records of the distances 100m backstroke and 200m backstroke. In 2001, she was inducted into the Hall of Fame International Swimming Sports.
Your world record over 200 meters back, she set up in Athens in 1991, was only after more than 16 years broken by Kirsty Coventry.
- European Athlete of the Year 1992
- World Swimmer of the Year 1991, 1992, 1995
- European Swimmer of the Year in 1990, 1991, 1992, 1995
- Hungarian Sportswoman of the Year 1988, 1989, 1990, 1991, 1992, 1993, 1996
- 1992 - Commander of the Order of Merit of the Republic of Hungary