A valve-stroke control apparatus continuously varies the stroke of a valve in an engine, and selectively maintains it in a closed position, while the engine is in operation. The control apparatus includes a force-transmitting rod which is pivoted by a cam and a cam-contact roller. An additional roller on one end of said force-transmitting rod engages a transverse contact surface of a stroke-length setting lever. The contact surface has a contour such that pivoting of the force-transmitting rod causes movement between the contact surface and the additional roller, which in turn displaces the force-transmitting rod longitudinally in a direction associated with valve opening. Such displacement is introduced by way of a rotary articulation into a rocking lever that activates the valve.