Magnetic fluids are colloidal suspension of ferromagnetic materials of about 10 nm diameter in a liquid carrier. Inverse magnetorheological fluids consist of non-magnetic particles (μm size) suspended in a ferrofluid. These particles form magnetic holes in the fluid phase. In addition to their scientific interest, magnetorheological fluids have attracted renewed attention in recent years due to interest in computer-controlled hydraulic systems and other applications. In this work we examine the behavior of the inverse magnetorheological systems in which particles exhibit magnetic dipole-dipole interaction upon application of the external magnetic field. In our experiments the ferrofluid is oleic-acid-stabilized, sub-domain (∼10 nm) particles of magnetite dispersed in kerosene carrier. The non-magnetic particles are Al 2O3 spheres and hollow glass beads of diameter ∼1 μm. The density of ferrofluids nearly matches to that of the dispersed particles, in this manner the gravity force plays a nearly negligible role in the structuring. Using optical microscopy and light scattering technique we demonstrate the formation of chain and column-like structures. Chain length distribution functions are estimated on the basis of the microscope images. Equilibrium and non-equilibrium molecular dynamics simulation methods are also applied to study the magnetorheological effect. (NVT ensemble molecular dynamics simulations are performed, in which the temperature of the system is kept at fixed value by a Gaussian thermostat. The equations of motion are integrated using a modified Verlet algorithm.) In the case of computer simulations the particle-particle interaction (in an applied magnetic field) is modeled by the dipolar hard sphere potential, where the dipoles are constrained to be parallel to a given direction (i.e. the direction of the external field). As the results of simulations, the pair distribution function and the chain length distribution are predicted. By the comparison of the experimental and computer simulation data, the validity of the applied model and the concentration and field strength dependence of the chain formation are discussed.