A method and a device for controlling the oil supply of an automatic transmission (gearbox) and to a starting element. The method can guarantee a sufficient supply of oil to a hydraulic control unit of the automatic transmission and/or the starting element, in particular an oil-cooled friction clutch, both during the operation of the internal combustion engine (4) and when the latter is at a standstill with the aid of an oil pump (2) that can be mechanically driven by the internal combustion engine (4) and a second oil pump (3) that can be electrically driven. In addition, the cooling oil supply of the starting element is guaranteed by the provision of a low-pressure oil by way of the electrically driven oil pump (3), at least during the starting operation, the stream cooling the starting element (11).