A hydrostatic drive system of a mobile machine includes a hydraulic work system and a hydraulic work pump that is driven by an internal combustion engine and, when operated as a pump, takes in hydraulic fluid with a suction side from a tank and, with a delivery side, delivers into a delivery line that leads to the hydraulic work system. A bypass valve is provided with which, when the hydraulic work pump is operated as a motor to start the shut-off internal combustion engine, the volume flow delivered by the hydraulic work pump operated as a motor to the delivery side is diverted to the tank. The bypass valve, in the motor operation to start the shut-off internal combustion engine, is actuated into an open position that connects the delivery side of the hydraulic work pump with the tank.