Photocurrent oscillations, observed at low temperatures in lattice-matched Ga1-xInxNyAs1-y/GaAs multiple quantum well (MQW) p-i-n samples, are investigated as a function of applied bias and excitation wavelength and are modelled with the aid of semiconductor simulation software. The oscillations appear only at low temperatures and have the highest amplitude when the optical excitation energy is in resonance with the GaInNAs bandgap. They are explained in terms of electron accumulation and the formation of high-field domains in the GaInNAs QWs as a result of the disparity between the photoexcited electron and hole escape rates from the QWs. The application of the external bias results in the motion of the high-field domain towards the anode where the excess charge dissipates from the well adjacent to anode via tunnelling.