A main rocker arm which is pivotally mounted on a rocker shaft has one or more sub-rocker arms pivotally mounted thereon. The main rocker arm is arranged to synchronously open and close two poppet valves. Each of the sub-­rocker arms can be selectively locked to the main one by way of hydraulically operated plunger arrangements. The main rocker arm is provided with a roller type cam follower which follows a low speed cam. The sub-rocker arms are provided with followers which engage high or very high speed cams. Lost motion springs which maintain the sub-rocker arms in contact with the cams are mounted on the main rocker arm.