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In this work the effect of a homogeneous magnetic field on the dielectric permittivity and magnetic susceptibility of MRE based on silicone rubber and various magnetic filler (Fe, NdFeB and Fe3O4) was studied. The dielectric permittivity was calculated from the measurements of the capacity of a plane capacitor filled with MRE sample in the frequency range from 1 to 200 kHz. The magnetic field up to 0.5 T was applied in two geometries (in plane and out of plane of the capacitor). A giant increase of the capacitance (magnetodielectric effect) was observed when the applied field was perpendicular to the capacitor plates. The value of the magnetodielectric effect strongly depends on the type of magnetic filler as well as on the size and concentration of magnetic particles within MRE composites. The highest magnetic response reaching 150% was observed for the MRE based on magnetically hard NdFeB filler. A simple model explaining physical reasons for the magnetodielectric effect in MRE is proposed. The magnetic susceptibility of MRE also found the non-monotonic dependence on magnetic field under orthogonal orientation of static and alternative magnetic field. The theoretical consideration indicates to the resonance origin of this effect and is in qualitative agreement with experimental results. The found effects was found to be nonlinear dependent on the concentration of concentration of magnetic particles due to the interaction between them. The found peculiarities are discusses as well as possible practical applications of studied materials.