A method for supplying fluid to a transmission component such as a transmission control unit, a transmission lubricating system, and/or a transmission cooling system. The transmission is an automatic transmission of a motor vehicle having a hydraulic actuating system. A hydraulic medium is drawn from a region within the interior of a transmission case by a positive displacement pump, and the region of the transmission case from which the positive displacement pump draws the hydraulic medium is subjected to an overpressure that is somewhat greater than the ambient pressure around the transmission case.