The invention relates to a device for the variable actuation of the gas exchange valves of internal combustion engines, whereby a continuously revolving cam drives an intermediate member which carries out an oscillating, pure rotational movement and moves a drive member in accordance with the respective valve lift curve via a control cam. In order to modify the valve lift curve, the position of the rotational axis of the intermediate member can be modified along an advance curve. The rotational axis of the intermediate member is represented by a pin which is freely rotatable at its guide end and which carries cam plates that are linked therewith in a rotationally fixed manner. Said cam plates define either directly or indirectly the respective required position on the advance curve. The pin is rotated via a suitable joining element.