Using the well known approach of feedback linearization, we study problems that can be applied to controlling the rotational motion of a pair of human eyes. Eyes move to acquire a fixed point target and the control task is to direct the eye-pair towards a general target direction and, if the target is close by, to focus on the target. Roughly speaking, the former task is accomplished by versional eye movements and the latter task of pinpointing the eye on a specific target is accomplished by vergence eye movements. In this paper, we separately synthesize asymptotically stabilizing controllers, in the neighborhood of a target point, for version and vergence control systems. This is accomplished by defining a suitable output and regulating the output to the origin, while the eyes gaze towards the target.