A valve actuating mechanism which can be set to three different strokes for a gas exchange valve includes a finger lever actuated by a control cam with a single lift curve, with the finger lever being selectively connectable to a longitudinal guide in the region of its bearing member via incorporation of a piston that is movable in various positions. In a first coupling position of the piston, the bearing member is fixed to the longitudinal guide so that the finger lever executes a maximum pivot during the lift phase of the cam. In a second coupling position of the piston the finger lever is moved axially along the longitudinal guide during a complete cam lift so that the opening cross section of the gas exchange valve is smaller than in the first coupling step. In a third coupling step of the piston, the finger lever executes an idle stroke-pivoting movement on its point of contact on the gas exchange valve which remains closed.