In 1990, he received the Boris Blacher Prize and won a Cité internationale des arts scholarship for 1990/91 in Paris.
His study of music theory as well as the philosophy and history of art assured him acquisition of the Magistertitels title.
As a composer, he is by performances with the citizens of Berlin Biennale, Wiener Festwochen (Vienna's week-long musical festival), the Wittener Tage für neue Kammermusik and in Donaueschingen.
He has also performed for Südwestfunk Radio in Baden-Baden, the Konservatorium in Basel and the Steirischen Herbst, the Schleswig-Holstein Musik Festival, Sender Freies Berlin and the Süddeutscher Rundfunk.
Since 1997, Kyburz has served as professor for composition at the Hochschule für Musik "Hanns Eisler" in Berlin.