We have investigated the magnetoresistance (MR) of high mobility, near surface two-dimensional electron gases that are subject to a periodic magnetic field of amplitude up to 0.3 T. The fields are produced by sub-micron arrays of ferromagnetic stripes on the surface of the heterostructures. For small applied external magnetic fields we observe an MR of up to 1500% in applied fields of ∼100 mT. At low temperatures we observe both commensurability and Shubnikov-de Haas oscillations in the same field range. The SdH oscillations are strongly modulated by the 1D periodic magnetic potential. The observed behaviour is not consistent with semiclassical models. A new type of MR is observed on increasing the amplitude of the modulation. In this case, the MR amplitude increases as T2. This provides evidence of an electron–electron scattering contribution to the resistivity possibly due to the presence of minibands.