Upon graduating in 1971 and earning his master's degree in 1977, Trajković attended Andre Laporte and Witold Lutoslawski's international summer course in Grožnjan, Croatia.
Among other notable Serbian composers, Katarina Miljković, Isidora Žebeljan, Ognjen Bogdanović, Anja Đorđević, Melinda Ligeti, Božo Banović and Aleksandar Sedlar Bogoev have all either graduated or earned their master's degree under Trajković's supervision; his student was also Đuro Živković.
In the domain of musicology, and in collaboration with Slobodan Varsaković, he undertook to fully restore the bequest of his grandfather, Miloje Milojević, by classifying his numerous manuscripts, compositions and papers into a comprehensive catalogue.
Arion, Le Nuove Musiche Per Chitarra Ed Archi (1979) is regarded as the key achievement of this style's early phase in Serbian music; here the composer applies the postmodern repetitiveness to a chord progression originating in extended jazz modality, building a clear musical form in which quasi-improvisational guitar solos alternate with an extremely slow succession of chords introduced by the strings.
Trajković's most recent body of work demonstrates a certain settling and "academisation" of the style accompanied by an exceptionally adroit profiling of expert technical treatments.
Zephirus Returns (2001) recycles and, by means of post-modern stylisation, "disintegrates" the Franco-Italian flavour by hybridising Monteverdiesque patterns and post-impressionist expression.
The objectivism of it, the serenity undisturbed by any subjectivist engagement, the image of one "perfect world" unshaken by the human and the too-human, is perhaps (neo)classical, with all the recognisable topography of the four-movement sonata cycle.