A device for operating a starter mechanism actively connected with a hydraulic supply circuit of a transmission unit. The starter mechanism has a piston chamber subject to hydraulic pressure for activating a frictional shift element and a hydraulic chamber subject to hydraulic pressure for the cooling and lubricating an area of the starter mechanism. A hydraulic pressure between a lubrication pressure control port of a second pressure relief valve and the hydraulic chamber and equivalent to a lubrication pressure, is exerted on a second back pressure outlet port of a first relief valve, which acts on a valve slide of the first relief valve in the opposite direction relative to the working pressure exerted on a first back pressure outlet port of the first relief valve so that the pressure feed-back of the hydraulic pressure to the first relief valve occurs additively to the pilot signal characteristic of the first relief valve.