Avshalomov received his education at the Zurich Conservatory. In 1914 he moved to China and began his study of native Chinese music.
This study prompted him to incorporate Chinese subjects and themes into his work. The operas =Kuan Yin= and =The Great Wall= are examples of his compositions from this period. He took up residence in New York in 1947 and continued to compose, producing ballets, symphonies and concerti for violin and piano.