The contribution of two types of cascading process to the nonlinear optical diffraction of electromagnetic waves from a standing acoustic wave in a GaAs crystal is theoretically studied. The first type of cascading process results from second-harmonic generation followed by linear acousto-optical diffraction, while the second type involves linear acousto-optical diffraction from the standing acoustic wave and subsequent sum-frequency generation. In contrast to the third, direct, nonlinear acousto-optical diffraction processwe previously investigated, the photoelastic interaction between electromagnetic and acoustic waves is here linear. We establish the rules governing the cascading processes and show that in most cases the output signal simultaneously results from two or even three of the possible nonlinear diffraction mechanisms. However, we demonstrate that a careful choice of the incidence angles of the incoming electromagnetic waves, of the polarization combinations of the incoming and diffracted waves, and of the type of acoustic wave (longitudinal or transverse) makes it always possible to distinguish between the direct and either of the two cascading processes.