Abstract: The invention relates to a method of growing a GaAs film on the surface of a Si or GaAs substrate by exposing the growing surface of the substrate in a vacuum to at least one vapor beam containing the Ga elementary component of the GaAs compound, and to at least one vapor beam containing the As elementary component of the GaAs compound. The method is characterized by the steps of (A) growing a GaAs buffer layer by alternately applying the elements of the GaAs compound to the surface of a substrate heated to a first temperature one atom layer at a time, whereby in the formation of each atom layer the growing surface is exposed to a vapour beam containing one elementary component of the GaAs compound only; and (B) heating the substrate to a second temperature higher than the first temperature, and growing another GaAs layer on the buffer layer by applying both of the elementary components of the GaAs compound simultaneously.