Klusák was born to a Czech Jewish family, who owned the farm in Prague (Prosek). After he graduated from the gymnasium, he pursued his studies at the Prague Music Academy as a pupil of Jaroslav Řídký and Pavel Bořkovec (in 1953-57). Later he concentrated solely on composing.
He has never worked directly with music groups or schools, although his style was temporarily influenced by the music of Sergei Prokofiev and Igor Stravinsky, and later by the Second Viennese School, especially by Alban Berg and Serialism. Since 1959 he cooperated closely with Czech conductor Libor Pešek and with Chamber Philharmony. In the 1960s he occasionally acted in films, such as the 1966 film A Report on the Party and the Guests, in addition to composing the music. However, after the Warsaw Pact invasion of Czechoslovakia in August 1968, Klusák was condemned as a "politically undesirable" person (he composed music for prohibited films). During the normalization Klusák was engaged in the Jára Cimrman Theatre, but he was forced to leave in 1975. Following the Velvet Revolution in 1989, he began to participate in public life again, and worked as a member and director of various cultural institutions in the Czech republic. He was awarded a "Classic 1995" Award for his compositions and for his String Quartet No. 5 in particular.
- Partita for viola solo (1954)
- Concertino for flute, violin, viola and cello (1955)
- Contrappunto fiorito for flute, English horn, clarinet, bassoon, violin, viola, cello and piano (1955–1956)
- Osm invencí (Eight Inventions for Various Instrumental Arrangement) (1961–73) - his key work
- Čtyři malá hlasová cvičení na slova F. Kafky (Four Little Voice Exercises to the Words of Franz Kafka) (1960)
- Obrazy pro 12 dechových nástrojů (Images for 12 Wind Instruments) (1962)
- Variace na téma Gustava Mahlera (Variations on the Theme of Gustav Mahler) (1962)
- Smyčcový kvartet č. 2 (String Quartet No. 2.) (1962)
- Rejdovák for bass clarinet, viola and double bass (1965)
- Sonáta pro smyčcové a dechové nástroje (Sonata for String and Wind Instruments) (1965)
- Le forgeron harmonieux : variace na Händlovu árii : per grande orchestra (variations on George Frideric Handel's The Harmonious Blacksmith) (1966)
- Rondo pro piano (Rondeau for Piano) (1967)
- Radix nativitatis I.S. for voice, flute, clarinet, viola and piano (1972)
- Duet pro flétnu a piano (Duet for Flute and Piano) (1977)
- Luna v zenitu (Zenith Moon), 4 Poems of Anna Achmatová for mezzo-soprano, clarinet, viola and klavier (1981)
- Monolog „Ubi vult“ (Monologue "Ubi vult") for viola solo (1987)
- String Quartet No. 4 (published 1994, premiered 2001)
- String Quartet No. 5 (premiered 1970)
- String Quartet No. 6 (premiered 1970)
In the 1980s Klusák focused more on vocal compositions. He began to compose song cycles, cantatas, and wrote an opera.
- Cokoli chcete (Whatever you want) (1986) - opera
Klusák is also the composer of the music to the popular Czech television series Hospital at the End of the City.
- Vysloužil, p. 256
- Jan Klusák English
- See e.g. OCLC 24485066 for a description of the 1969 Panton publication.
- Musicbase.cz Quartet 4 Page
- Musicbase.cz Quartet 5 Page
- Musicbase.cz Quartet 6 Page
- Vysloužil, p. 257
- Description with audio samples of the Supraphon Recording of Klusák's String Quartets from Supraphon.cz