Since für Cello solo (written 1964), he has composed in all genres, including many pieces for unaccompanied solo instruments and theatre works. He has always remained outside of the mainstream and has never been associated with any of the many movements in postwar European music, though he did attend summer courses at Darmstadt in the 1980s. Today, Hespos is still relatively unknown in the United States.
Even by the standards of the European avant-garde, Hespos' music usually is quite extreme and unconventional. In his many pieces for solo instruments, Hespos pushes instruments to their timbral limits, employing extended techniques and other effects to create unusual sounds (For example, Duma (1980) for alto flute requires the performer to spit into his or her instrument to create sickly gargling sounds). He frequently writes for less-common instruments, such as cimbalon (1976's Cang) or musical saw (used in Ganifita-Blues, 1984). He even calls for extreme stage techniques in his theatre works—the famous piece Seiltanz ("Tightrope Dance", 1982) requires an actor to break his way out of a metal cage by means of a welding torch.
Hespos' scores very frequently employ graphic notation, verbal instructions, traditional music notation or some combination thereof. Many of his works involve improvisation. Additionally, Hespos' music must often be performed without a conductor, putting even greater demands on the performers.
Hespos has been the recipient of many awards and honors in his career, including the 1967 Gaudeamus International Composers Award and a scholarship to study at the Villa Massimo in Rome in 1972. In the year 2005, the Akademie der Künste, Berlin created an archive of Hespos' music. That same year, Opera World magazine selected Hespos' iOPAL as the opera premiere of the year.