Radica taught at the Sarajevo Music Academy from 1959 to 1963, and then joined the faculty of the Zagreb Academy, lecturing in musical theory.As a composer, Radica's early style was essentially neo-classical; in the Grove Dictionary of Music and Musicians, Nikša Gligo instances the compositions in Cetiri dramatska epigrama (Four Dramatic Epigrams, 1959), and the Concerto abbreviato (1960).
After this, Radica came under the influence of Leibowitz, a strict follower of Arnold Schoenberg's dodecaphonic theories.
Gligo gives Lirske varijacije (Lyrical Variations, 1961) as an early example of this aspect of Radica's style.
Radica has also experimented with Aleatory techniques.
In his K a (Towards A), for two instrumental groups and synthesiser (1977) he aimed to reinstate melody.
Gligo comments that some of Radica's later works, with a focus on the relation between speech patterns and "motivic musical ideas", have a style reminiscent of Janácek and early Stravinsky.Radica's works include several ballet/dance scores, large-scale orchestral pieces, chamber and choral music and songs, and an opera, Prazor (The Dawn, 1991).