From 1950 to 1961 he attended Kharkiv Music High School, and from 1961 to 1962 the Kharkiv Conservatory where he studied composition with Dimitri Klebanov and piano with V. Topilin. From 1962 to 1966 he studied composition with Nikolay Peyko and piano with Anatoly Vedernikov at the Gnessin Institute in Moscow.
He emigrated to Germany in 1981. At the age of four (1946) Suslin began to study piano and made his first attempts at composition. He worked as an editor at the publishing house Muzyka in Moscow (1966–1980).
In 1969 his piano sonata was given an award at the Young Composers Competition.
In 1971 his music was performed outside of Russia for the first time at the Festival de Royan, France. Suslin taught instrumentation at the Moscow Conservatory (1972–1975).
In 1975 he founded the ‘Astraea’ improvisation ensemble together with Vyacheslav Artyomov and Sofia Gubaidulina. Suslin emigrated to West Germany in 1981.
From 1984 he worked as an editor at Musikverlag Hans Sikorski, Hamburg.
From 2007 Suslin was director (Geschäftsführer) of Musikverlag M. P. Belaieff.
Suslin became a member of the Union of Soviet Composers in 1967.
