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In tracking repetitive square waves, the latency of saccadic eye movement to a change in target position decreases as the tracking run progresses. The latency in the steady state takes its minimum value for frequencies between 0.5 and 1.0 Hz. A model is proposed to predict this behavior of the saccadic eye movement system. Forming an estimate of target motion and carrying out the optimal control based on the estimation are the main features of the model. The estimate, in particular that of the period of square waves, is assumed to be performed with some inevitable variance depending on the input frequency because of the sampled data nature of the system and the memory mechanism becoming more uncertain with increasing time. In relation to sinusoidal target motions, a similar model is suggested to explain the reduction of latency to the steady-state value soon after the onset of target motion. Further, the transfer characteristics in the steady state are obtained for both the open-loop and closed-loop systems. It turns out that in both cases the predictive controller can be approximated by a serial connection of a high-gain element and a predictive element.