Highly resistive dusts show markedly non-ohmic properties. The property known as specific resistivity is strongly dependent on the dust layer thickness and on the polarity of the high voltage. The current transport occurs by excess charges of both polarities, which leads to high space charge densities and induces strong electrostatic fields. The theory of electrets provides a consistent explanation of the phenomena observed so far. To investigate the electrical properties, highly resistive dusts were exposed to an electrical field with interfering corona discharges within a tip-plate arrangement.