A hydraulic system for controlling a belt-driven conical-pulley transmission of a motor vehicle, wherein the transmission has a variably adjustable transmission ratio. The hydraulic system includes a first valve arrangement to control a contact pressure in the belt-driven conical-pulley transmission, a second valve arrangement to control the transmission ratio of the belt-driven conical-pulley transmission, and a hydraulic energy source to supply the hydraulic system with hydraulic energy. In order to provide an improved hydraulic system, the system includes a third valve arrangement for controlling a forward clutch and a reverse clutch, and for controlling a parking lock.