A control device for a gas exchange valve of an internal combustion engine having a multi-membered transmission comprising at least one driving element (1), actuating elements (2) each of which actuates one gas exchange valve (3), a transmission element (9) which is hinge-connected between the at least one driving element (1) and an actuating element (2) which acts on a gas exchange valve (3), a cam joint (15) between the transmission elements (9) and an area of the housing (5) of the control device, in which a first bearing area which is provided on the transmission element (9) and a second bearing area which is provided in the housing area are adjustable with respect to one another during operation of the engine, is to be manufacturable easily for extremely accurate operation. To this end, such a control device is characterized in that the second bearing area of the cam joint (15) forms the radial inside surface of a circular arc-shaped link element which is supported so that it is diplaceable in the direction of the circular arc with a circular cylindrical peripheral surface on the outside radially in a complementary guide surface of the house of the control device.