Swollen physical magnetorheological (MR) gels were obtained by self-assembly of triblock copolymers containing dispersed magnetic particles. We carry out a detailed investigation of the nonlinear rheological properties of MR gels under large amplitude oscillatory shear flow. A strong Payne effect is observed for strains above 0.05% which is the limit of linear viscoelastic region. The onset strain for the transition from linear to nonlinear viscoelastic behaviour is much smaller than in the absence of a magnetic field. We show that the magnetic Payne effect strongly depends on the magnetic flux density, the particle volume fraction, the sample's initial particle distribution and viscoelastic properties of the matrix. The rheological response of MR gels is strongly related to the ability for rearrangement of the particles in the presence of the magnetic field. Upon sudden application of a magnetic field, the particle network embedded in a soft matrix becomes more anisotropic than is the case in a hard matrix since the resistance of the matrix to particle rearrangement is smaller. The induced anisotropic particle network parallel to the field provides larger absolute rheological response. (C) 2012 Elsevier Ltd. All rights reserved.