Composed ballets based on the classics and won the Lenin in 1984, the USSR State Prize in 1972, and the State Prize of the Russian Federation in 1992.
His early works mixed folk music with tonal music. He also incorporated aleatoric and serial techniques.
He wrote the ballet Carmen Suite in 1967, which was based on Georges Bizet's opera. His 1971 ballet Anna Karenina was based on the Leo Tolstoy novel. His 1976 ballet Dead Souls was based on the novel by Nikolai Gogol.
His family was very musical. His father taught music theory and also composed music. He married ballerina Maya Plisetskaya in 1958.
He was inspired to compose 24 Preludes and Fugues after hearing the similar works of Dmitri Shostakovich.