We investigated horizontal smooth pursuit eye movements and hand movements in tracking tasks in order to find out whether hand movements influence eye movements and if so, in what ways. Externally controlled target movements were tracked either by the eyes alone or by the eyes and right hand together. Because a possible influence might depend on the stimulus, we used two classes of target movements: sinusoidal target movements (predictable target movements) and pseudo-random target movements (unpredictable target movements). Our data show that the eye movements contained only a few small saccades when sinusoidal target movements with frequencies higher than about 1 Hz were tracked by eyes and hand together. More and larger saccades were made when the same target movements were tracked by the eyes alone. The difference in smoothness of eye movements was highly significant between the two tracking conditions. Such a difference was not found during the tracking of a pseudo-random target motion. This suggests that the influence of hand movements is related to the predictability of the stimulus. In contrast to the gain of the smooth pursuit eye movements and the maximum of the cross-correlation function, the gain of the composite eye movements did not depend on the tracking condition. The delay of the eye movements with respect to the (sinusoidal) target movements also showed no dependence on the tracking condition. Visual feedback from the tracking hand was found not to play a role in the difference in eye movements for the two tracking conditions.