In 1966 Globokar joined a performing group for new music at SUNY (Buffalo), and in 1968 he was appointed to teach the trombone at the Staatliche Hochschule für Musik in Cologne and composition at the Cologne Courses for New Music. He founded the Free Music Group in 1969 and a quartet, New Phonic Art, also in 1969, both of which perform contemporary music, including many of his own works. He also performed in Stockhausen’s group, and from 1973 to 1979 was head of vocal-instrumental research at IRCAM, Paris. His phenomenal virtuoso technique on the trombone attracted many composers to write for him, among them Stockhausen (trombone version of Solo), Berio (Sequenza V) and Kagel (Atem and Morceau de concours) as well as René Leibowitz, Louis Andriessen, Jürg Wyttenbach and Toru Takemitsu.
His compositions total over 100 pieces. His solos, chamber music, orchestral and choral pieces, as well as his music for theatre, are published by CF Peters and Ricordi. His music often involves extended performing techniques, an intensely theatrical sensibility as well as an ever present sense of humor. He lives in Berlin.