Creation of and the following research on systems featuring elastomer filled with a magnetic disperse material with good electroconductive properties have been a continuation of the development of magnetorheological fluids with the goal of finding compositions exhibiting a stronger magnetorheological effect. More profound investigations have revealed that composite materials of the given type also exhibit other significant features such as magnetodeformation, magnetostriction, field-induced shape memory, and piezomagnetoresistance, for which reason they are frequently classified as ‘magnetoactive elastomers’. Within the frames of this work, investigations of relationships between the electroconductive and dielectric properties of the polymer composite and external magnetic fields have been done. As has been shown by the experiments, changing the external magnetic field from zero to 330 mT causes the best samples to improve their conductive properties by six orders of magnitude. At the same time, the capacitance measured along with the resistance increases by a factor of 30. Reproducible and less subjected to the emergence of runouts at frequencies of 1 kHz and higher, the capacitance-based data offer hope that such elastomers may be good candidates for being employed as sensors. In order to make the sample-dependent results comparable, the capacitances are interpreted as the dielectric permeabilities. It should be noted though that this approach is strictly formal and the mechanism of the phenomenon observed still awaits its scrupulous study.