The invention relates to an electromotive device for operating gas exchange valves on internal combustion engines, comprising a rotary actuator exerting forces on one or more valve stem ends of one or more gas exchange valves by means of a lever arrangement. The rotary actuator is a reluctance motor with a cylindrical iron rotor with permanent magnet segments of alternating magnetisation arranged on the circumference thereof. The average angular separation of the poles of the stator of the reluctance motor are approximately equal to the average angular separation of the permanent magnet segments on the rotor. The valve shaft ends operated by the lever arrangement preferably belong to gas exchange valves of a cylinder of an internal combustion engine the opening times of which do not coincide or belong to gas exchange valves on different cylinders. The reluctance motor preferably has a single-phase design. The device permits a valve clearance adjustment of the gas exchange valves by control of the actuator current and carrying out part lifts. The electromotive device for operating gas exchange valves is space-saving, low in energy consumption nd wear and self-retaining in certain working positions.