Despić studied composition with Marko Tajčević and conducting with Mihajlo Vukdragović between 1950 and 1955 at the Music Academy in Belgrade.

[1][2] Despić was a full member of the Serbian Academy of Sciences and Arts (SANU).

[3] Despić was the author of more than 240 compositions - with a special penchant for concertante genres and chamber music[2] – and an opera, in addition to several scientific and theoretical studies, and numerous textbooks (music theory, harmony, harmony analysis, orchestration) for both school and university level.

[4] Despić won many awards for his music; his "Manchester Trio for flute, violoncello, and piano, Op.

166, for English horn and chamber orchestra" (2005) – for which he won the "Mokranjac Award" – have been particularly singled out.