We have examined the small strain response of an inverse ferrofluid system, consisting of micron-sized inert particles dispersed in a ferrofluid, which is a magnetisable liquid consisting of single domain magnetite nanoparticles. Under a magnetic field the inert particles will form elongated aggregates in the field direction, analogous to a magnetorheological fluid. It was found that the fluid appeared to have a Bingham fluid-like yield stress when analysed using the flow curve. However careful study of the behavior at very low shear rates revealed an ever decreasing shear stress. In addition, the behavior of conventional magnetorheological fluids at large strains under steady shear flow and constant magnetic field was also studied, and the results compared to particle-level computer simulations.