Osor Musical Evenings is jointly organized by the association of the same name, based in Osor and Zagreb, and the Pula Open University from Mali Lošinj. The cooperation between the Association and the local community dates back to the very beginnings of the festival in the second half of the 1970s. The current Management Board of the Osor Musical Evenings Association, chaireded by Lovro Marušić, consists of Martina Lipovac, Josip Nalis, Sanda Majurec, Branko Mihanović, Marin Marušić, Marija Saraga, Matko Marušić, and Berislav Šipuš.

The first statute of the Association and the programme objectives of the festival were drawn up by Vladimir Seljan, Ivo Horvatić, Stjepko Huml, led by Daniel Marušić, who was the spiritus movens of the festival until his death in 2009. At their invitation to join forces in founding a new classical music festival, Lošinjska plovidba soon responded, led by director Ivo Jureković, while Zlatko Stahuljak and Kazimir Brunović provided professional assistance from the very beginning.

The first Artistic Council, established in 1976, was chaired by Andro Mohorovićič and consisted of Stanko Horvat, Jasmina Juračić, Vojko Kiš, Vladimir Kranjčević, Rado Manzoni, Adalbert Marković, Daniel Marušić, Miroslav Miletić, Zlatko Pibernik, Vida Ramušak, Mladen Raukar, Vladimir Seljan, and Zlatko Stahuljak.

Since 2011, when Osor Musical Evenings was granted the status of a national festival, the artistic director has been appointed by the Ministry of Culture and Media of the Republic of Croatia, which also oversees the festival council tasked with monitoring and supervising the festival's work.