Relationships inherent in the processes that occur at the initial stage of a high-voltage (electric field strength E >1MV cm) gas discharge with participation of nonmetal nanofilms adsorbed to the cathode are considered. It is shown that the current-voltage characteristic of the prebreakdown current obeys the Fowler–Nordheim equation corrected for the quantum character of image forces. Based on electronic polaron theory, a general expression for the field emission current at the contact of between two media is obtained. It is shown that for the above-mentioned fields, the field dependence of the tunnel current is appreciably different from the well-known classical relations.