Photorefractive quantum wells are nonlinear materials characterised by high sensitivity and a fairly fast response (≈ <i>μs</i>) at relatively low densities of optical power (<i>μW/cm<sup>2</sup></i>). For structures working in the Franz-Keldysh geometry (with the electric field parallel to quantum wells) observed phenomena are related to the nonlinearity of electrons transport, i.e. the dependence of electron mobility on electric field intensity. This phenomenon plays an important role in photorefractive two-wave mixing, causing the shift of the space-charge field relative to the interference pattern, which allows obtaining high photorefractive gain, reaching 1000 cm<sup>-1</sup> for E=10 kV/cm. One of the parameters of SI-MQW structures that affects nonlinear transport is the electron and hole trapping coefficient. In the literature describing the processes taking place in GaAs/AlGaAs quantum wells that value is presented as constant. In article, the authors describe experiments testing the effect of strong electric field on the electron and hole trapping coefficients for bulk GaAs. An analysis of how the electric field-dependent trapping coefficient affects the process of two-wave mixing in MQW structures is discussed in. The results presented therein relate only to the stationary interference pattern. However in some studies the shift of the electric field distribution relative to the distribution of light intensity is obtained by using a moving interference pattern. We present the results of a numerical analysis of the impact of the electric field-dependent carriers trapping coefficients on the space-charge field formation under a moving grating.