In 1955 Zivanovic founded Mihajlo Zivanovic’s Octet in which he played the baritone saxophone. Alongside him, Predrag Ivanović played the trumpet, Nikola Dajzinger the alt saxophone, Eduard Sađil the tenor saxophone, Predrag Stefanović the trombone, Vojkan Đonovićić the guitar, Robert Hauber the piano and Rade Milivojević the drums.
Octet had been performing for 10 years with great success on radio stations in the country and abroad. It soon became one of the leading Yugoslav ensembles for contemporary and experimental jazz music.
Since 1958 almost to the last days of his life, he had been employed by the Music Production branch of Radio Television of Serbia. That same year he became a permanent member of the Light String Orchestra led by Ilija Genić and later a conductor of the Jazz Orchestra i Revue Orchestra of Radio Television Belgrade.
In 1960 he became a member of Serbian Composers Association.
In 1975 he was appointed head of the Light Ensemble of RTB, and since 1978 permanent conductor of the Light Orchestra of RTB until his death.