A device for controlling gas-exchange valves of an internal combustion engine is provided, which device has hydraulic valve actuators each allocated to one gas-exchange valve. Each valve actuator has an actuating piston acting on the gas-exchange valve, and two hydraulic working chambers delimited by the actuating piston, of which the first working chamber acting upon the gas-exchange valve in the closing direction is constantly filled with fluid under pressure, and the second working chamber acting upon the gas-exchange valve in the opening direction is able to be alternately filled with fluid under pressure and relieved via two electric control valves. For the purpose of cost reduction, provided for each valve-actuator pair is a single first electric control valve that is acted upon with the fluid pressure on the intake side, and is connected on the outlet side to the second working chamber of one valve actuator. The second working chamber of the other valve actuator is filled with fluid with the aid of a switchover valve and the fluid pressure in the second working chamber of the one valve actuator.