Evgeny Mogilevsky was the grandson of Leonid Yakovlevich Mogilevsky. Leonid Mogilevsky was a Ukrainian conductor, trumpeter, and music teacher who taught at the Odessa Conservatory and became its professor in 1947.
Leonid Mogilevsky is described as the founder of a musical dynasty: his daughter was the music teacher and pianist Serafima Mogilevskaya, and his grandson was the pianist Evgeny Mogilevsky.
