An apparatus for controlling gas exchange valves includes at least one valve positioner, associated with a gas exchange valve, and a pressure supply device which supplies the valve positioner with a fluid under high pressure. The valve positioner encompasses a working cylinder having a positioning piston, coupled to the gas exchange valve, which delimits an upper pressure space for opening the valve and a lower pressure space for closing the valve, and encompasses a control valve controlling the hydraulic pressure in the pressure spaces. In order to reduce the manufacturing costs and electrical energy demand of the apparatus, the upper pressure space is connected directly, and the lower pressure space via a restrictor throttle, to the pressure supply device; and the control valve is connected to the lower pressure space and to a relief line. Depending on the switch position, the control valve additionally connects the lower pressure space to the relief line or blocks it off from the relief line.