Stationary and transient behaviour of photorefractive multiple quantum well structure illuminated by interfering plane waves of near resonant frequency was investigated in frames of photogeneration, diffusion, drift and trapping (PDDT) model. The influence of high intensity electric field applied along the quantum wells planes was considered and an effect of a nonlinear transport of electrons, characteristic for GaAs/AlGaAs samples, was included. An analytical expression for the fundamental amplitude of space-charge field in the sample and the dependence of the photorefractive grating response time on material parameters in the case of low interference pattern contrast is presented and compared with the earlier results.