Control theory principles have been used to gain understanding on how the different components of the oculomotor system operate. The purpose of this paper is to use the knowledge about how the visual system organizes these components to propose a new tracking paradigm.The tracking system is assumed to be described by linear time-invariant discrete-time state-space equations. The inputs to this system are the control action and the reference signal. The outputs are the controlled variable z and the measurements. The tracking objective is to keep \e(t)\ smaller than some prespecified value gamma, This is motivated by the organization of the human visual system, where the target should be kept within the fovea of the eye. The reference signal is modeled as the filtered version of a driving signal a(t), Its characteristics, together,vith the tracking objective, lead to the design of an optimal controller referred to as the "smooth pursuit controller."Since the tracking system should continue to operate in the event of a controlled variable constraint violation, a more complex control strategy is required. The approach in this paper, motivated by the behavior of the visual system, is to switch off the smooth controller whenever a violation occurs and design a time-optimal control action, i.e., a "saccade," to drive the control system so that the constraint is satisfied after the shortest possible time interval. After that, the smooth controller is switched back into the loop. The way this switching is performed is critical for obtaining "good behavior"; a method is proposed which is based on a careful definition of the target set for the saccade.The tracking system proposed in this paper is closely related to recent results in linear optimal and robust control theory. It also shows that the human visual system poses some very interesting questions and open problems which may stimulate further control theoretic work.