Eye-target synchronization is critical for effective smooth pursuit of a moving visual target. We apply the nonlinear dynamical technique of stochastic-phase synchronization to human visual pursuit of a moving target, in both normal and mild traumatic brain-injured (mTBI) patients. We observe significant fatigue effects in all subject populations, in which subjects synchronize better with the target during the first half of the trial than in the second half. The fatigue effect differed, however, between the normal and the mTBI populations and between old and young subpopulations of each group. In some cases, the younger (<or=40 years old) normal subjects performed better than mTBI subjects and also better than older (>40 years old) normal subjects. Our results, however, suggest that further studies will be necessary before a standard of "normal" smooth pursuit synchronization can be developed.