Hýsek played his first international tournament with the Four Hills Tournament in 1977/78 . He achieved his best placement on January 4, 1978 in Innsbruck with the 12th place. 2 years later he jumped in the ski jumping world cup for the first time . On January 27, 1980 he reached his first five World Cup points with 11th place in Zakopane . In his second and last World Cup competition in Gstaad , he also achieved World Cup points with 12th place. At the end of the 1979/80 World Cup season he finished 73rd in the overall standings with nine points.