[en] The beat wave accelerator depends on the generation of a large amplitude plasma wave with a phase velocity close to the velocity of light c. The plasma wave (ωsub(p), ksub(p)) is generated by beating colinear laser beams (ω₁, k₁) and (ω₂,k₂) with ωsub(p) = ω₁-ω₂, ksub(p) = k₁-k₂. Since the process involves both large amplitude transverse and longitudinal waves, various nonlinear instabilities associated with either wave may occur. The object of the article is to discuss some of the processes that may compete with the beat wave generation listing their threshold and growth rate. (author)