A mechanically controllable valve-train assembly includes a plurality of gas exchange valves, at least two cylinders assigned to each of the gas exchange valves, and valve-lift adjusting devices which each comprise a rotatable eccentric shaft. The eccentric shaft comprises at least one cam element and circumferential control surfaces which comprise at least one eccentric member. The eccentric shaft is driven by a drive device to set various valve-lift positions. A transmission assembly assigned to each of the gas exchange valves is mounted in a cylinder head via a bearing device so as to be movable and is operatively connected to one of the valve-lift adjusting devices and to a camshaft. The at least one cam element is operatively connected to a spring-loaded tappet element and is arranged outside the circumferential control surfaces and at a level of a zero-lift position of the circumferential control surfaces.