A valve drive device has a camshaft which includes a shaft element and a cam piece which can be driven by the shaft element and a first cam effecting a first stroke of a valve and a second cam effecting a second stroke of the valve, and is displaceable in the axial direction of the camshaft relative to the shaft element between a first position, in which the valve can be actuated by the first cam, and a second position in which the valve can be actuated by the second cam, and has an electrically controllable actuator via which the cam piece is displaceable relative to the shaft element in the axial direction as a result of an electrical control of the actuator. The actuator pushes the cam piece alternately back and forth between the positions in the case of successive electrical controls occurring with the same polarity.