Born in Korea, he received his first musical training (cello and composition) in Korea and Japan. Active opposition to the Japanese occupation resulted in his being imprisoned until the end of World War II. After gaining his freedom, he spent a period teaching music at Korean high schools and universities. After 1956 he travelled to Europe to continue his studies in Paris and Berlin (with Boris Blacher), also attending the International Courses at Darmstadt. In 1964 he became a resident of West Berlin, from where he was abducted in 1967 by the regime of President Park of Korea. He was imprisoned, tortured and sentenced to death. He wrote the opera Die Witwe des Schmetterlings in his prison cell. He was released in 1969 in the wake of international protests by composers and diplomatic pressure. After his release he continued political activity on behalf of the restitution of democracy in his homeland. Since his return to Germany, he taught (1969) at the Hochschule für Musik in Hanover, becoming professor of composition at the Hochschule der Künste in Berlin (1970–85). He became
a German citizen in 1971. He was a member of the Hamburg and Berlin Academies of Arts and of the Academia Scientiarum et Artium Europaea, Salzburg. He received an honorary doctorate from Tübingen University and was an honorary member of the iscm.
He died in Berlin.

Selected works: Fluktuationen for orchestra (1964), Der Traum des Liu-Tung, opera after 14th-century Chinese drama (1965), Réak for orchestra (1966), Die Witwe des Schmetterlings (Butterfly Widow), opera after 16th-century Chinese texts (1968), Geisterliebe, opera to a libretto by Harald Kunz (1969–70), Piri for solo piano (1971), Sim Tjong, opera after a Korean legend (1971–72), Violin Concerto (1976), Flute Concerto (1977), Double Concerto for oboe, harp and chamber orchestra (1977), Octet (1978), Clarinet Concerto (1981), Exemplum in memoriam Kwangju for orchestra (1981), three Violin Concertos (1981, 1983–86, 1992), two Chamber Concertos (1990), Symphonies: No. 1 (1983), No. 2 (1984), No. 3 (1985), No. 4 Im dunkeln singen (1986), No. 5 for baritone and orchestra (1987), Quartet for Flutes (1986), two Chamber Symphonies (1987, 1989), Quartet for flute, violin, cello and piano (1988), String Quartet No.4 (1988), Konturen for orchestra (1989), String Quartet No. 5 (1990), Espace I for cello and piano (1992), Together for violin and double bass (1990), String Quartet No. 6 (1990), Espace II for cello, harp and oboe ad lib. (1993), Quartet for oboe, violin, viola and cello (1994).

Espace I, written in 1992 and premiered in Hamburg the same year, is one of Yun’s more accessible late works (only seven compositions were to follow before his death). It may even be interpreted as a moving meditation on the main note of C sharp. Proceeding from this pitch, the first section builds an enormous arc of tension that engulfs all the isolated pitches like a mighty stream. After several violent outbursts it subsides into an eight-bar field of pianissimo on C sharp and maintains this level of calm to the end of the piece, fading into the twilight. It is as if Yun, in the story of a single pitch, were once again recounting the forces of yin and yang, the primordial principles of Tao, and speaking to us about the order of the universe – limitless, infinite, ever caught in a process of change while remaining, as a whole, fixed and immutable.