Segregating a moving object from its visual context is particularly relevant for the control of smooth-pursuit eye movements. We examined the interaction between a moving object and a stationary or moving visual context to determine the role of the context motion signal in driving pursuit. Eye movements were recorded from human observers to a medium-contrast Gaussian dot that moved horizontally at constant velocity. A peripheral context consisted of two vertically oriented sinusoidal gratings, one above and one below the stimulus trajectory, that were either stationary or drifted into the same or opposite direction as that of the target at different velocities. We found that a stationary context impaired pursuit acceleration and velocity and prolonged pursuit latency. A drifting context enhanced pursuit performance, irrespective of its motion direction. This effect was modulated by context contrast and orientation. When a context was briefly perturbed to move faster or slower eye velocity changed accordingly, but only when the context was drifting along with the target. Perturbing a context into the direction orthogonal to target motion evoked a deviation of the eye opposite to the perturbation direction. We therefore provide evidence for the use of absolute and relative motion cues, or motion assimilation and motion contrast, for the control of smooth-pursuit eye movements.