The predictive component of human smooth pursuit was studied by perturbing sinusoidal target motion at unpredictable instants. The disturbances consisted of either a brief period of stabilization of the target on the fovea or a replacement of the sine by a ramp displacement for half a period. To minimize the effects of a possible change of the tracking strategy by the subject the transitions were masked and only the initial part of the response to the disturbance was analyzed. After stabilization on the fovea the eye oscillation continued at the frequency of the preceding target movement for about one half-cycle, whereupon the oscillation was rapidly damped. The mean unidirectional smooth eye acceleration was 70% of the mean unidirectional target acceleration prior to the stabilization. This suggests that during pursuit of a sinusoidal target movement about 75% of the oculomotor response is generated by predictive processes. When the sine was replaced by a ramp, starting at the velocity zero-crossing, the eye accelerated away from the target for ca. 180 ms irrespective of the frequency of prior tracking. In contrast, when the ramp started at the peak velocity of the sinusoidal target motion the eye accelerated away from the target for more than a quarter period. After foveal stabilization during pursuit of a pseudorandom stimulus, the eye continued to oscillate for less than one period at approximately the highest frequency present in the stimulus. The frequency characteristics of human smooth pursuit of predictable as well as unpredictable target motion were correctly simulated by a model, which derived its predictive properties from a lead element, tuned to the current frequency of the target motion.