In 1940 Edward Clark offered him the British premiere of Khachaturian's Piano Concerto in D-flat, with only a month's notice, but he was very busy and said he would not be able to learn it in time; he suggested Moura Lympany in his place.
His repertoire includes more than 40 violin concertos by composers such as Vivaldi, Bach, Mozart, Beethoven, Paganini, Wieniawski, Mendelssohn, Brahms, Tchaikovsky, Lalo, Sibelius, Karol Szymanowski, Khachaturian, Bartók, Stravinsky, Hindemith, Prokofiev, Shostakovich and also music of Slovenian composers.
Ajemian's career in contemporary music got its impetus from her Armenian heritage; she became known as a contemporary pianist after performing the U.S. premiere of Aram Khachaturian's Piano Concerto, which she chose to play based on the fact that Khachaturian was Armenian.
To commemorate Snitkovsky’s seventy-fifth birthday, recording company "Melodia" issued a set of CDs containing his recordings of Bach, Paganini, Schumann, Shubert, Liszt, Bartok, Stravinsky, Khachaturian, Ysaye, Debussy, etc.