The nature of spontaneous lateral composition modulation and its relationship to surface morphology during the growth of (AlAs)m(InAs)n short-period superlattices by molecular beam epitaxy are investigated as a function of the global strain between the short-period superlattice and (001)InP substrate. For samples grown under tension, transmission electron and atomic force microscopy reveal composition modulations along directions close to <310> coupled to a surface cusping. For samples grown under compression, we observe composition modulations roughly along the elastically soft <100> directions coupled to a surface rippling. For high strains (≥0.7%), with individual InAs layer thicknesses ≤1.6 monolayers, we observe weak or no composition modulations. © 1998 American Institute of Physics.