A valve drive of an internal combustion engine, with a camshaft including cams for actuating gas-exchange valves, wherein at least one cam, which includes several cam faces, is guided nonrotatably but with freedom of axial movement on the camshaft; wherein a stroke profile, which cooperates with an actuating pin for the axial displacement of the cam or cam piece, is assigned to the associated axially displaceable cam or an axially displaceable cam piece comprising several cams; and wherein the stroke profile of the axially displaceable cam or cam piece in question includes intersecting stroke curves. A guide element is assigned to the end of the actuating pin which can be introduced into the stroke curve of the stroke profile of the associated axially displaceable cam or cam piece, this guide element being supported in such a way that it can rotate or pivot around the axis of the actuating pin.