This followed by him touring extensively in the Soviet Union as well as in Germany, Poland, Denmark, Sweden, Romania, Portugal and Korea.

In 1957 he became a professor of the violin at the Kiev Conservatory (later renamed Tchaikovsky National Academy of Music) and taught there until the end of his life.

To Ukrainian Radio he left over 70 hours of recorded music, including Bach's Sonatas and Partitas, Paganini's 24 Caprices, 24 preludes by Shostakovich (Gorokhov's own arrangement), Violin Concertos by Beethoven, Tchaikovsky, Mendelssohn, Brahms, and many other.

The Concertos were presented in an original orchestration by Gorokhov, which most completely embodied the criteria of Paganini's virtuoso-romantic aesthetics in orchestra.

Gorokhov's playing received high praise from a number of prominent musicians including Pierre Fournier, Jacques Thibaud, Joseph Szigeti, David Oistrakh and others.