We study problems that can be applied to controlling the rotational motion of a pair of human eyes. Eyes move to acquire a point target and the control task is to direct the eye-pair towards the 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 eyes on a specific point is accomplished by vergence eye movements. A cost function that minimizes the control energy has been chosen and the corresponding optimal trajectories are synthesized. Using a binocular eye model, an optimal controller is implemented in the open loop, that controls the two eyes to track and focus on a stationary target.