From 1962 to 1966 he studied composition with Nikolay Peyko and piano with Anatoly Vedernikov at the Gnessin Institute in Moscow.
In 1971 his music was performed outside of Russia for the first time at the Festival de Royan, France.
In November 1979 after several performances of his works in Paris, Cologne and Venice, Suslin was publicly denounced and blacklisted as one of the "Khrennikov's Seven" at the Sixth Congress of the Union of Soviet Composers for unapproved participation in some festivals of Soviet music in the West.
Suslin was good friends with Galina Ustvolskaya toward the end of her life, exchanging letters with her and facilitating an interview with Thea Derks.
Sikorski ostensibly began to publish Ustvolskaya's works while Suslin was an editor there.