The human smooth pursuit eye movement system has a latency of about 150 msec. However, this study shows that humans can learn to perform zero-latency tracking of targets that move with continuous velocity and amplitude-limited acceleration. Superposition of eye velocity and target velocity records, for our unique target waveforms, demonstrated that the subject was using the correct waveform and not just approximating it with a sinusoid or some other simple waveform. Calculation of the mean square error between target and eye position gave a quantitative measure of how well the human can track. The mean square error between target and eye position was 0.32 deg2 for one thousand seconds of steady-state tracking by seven subjects. For several cycles at a time all subjects were able to reduce this error to less than 0.1 deg2.