It has been the matter of some debate why we can experience vivid dynamic illusions when looking at static pictures composed from simple black and white patterns. The impression of illusory motion is particularly strong when viewing some of the works of 'Op Artists, such as Bridget Riley's painting Fall. Explanations of the illusory motion have ranged from retinal to cortical mechanisms, and an important role has been attributed to eye movements. To assess the possible contribution of eye movements to the illusory-motion percept we studied the strength of the illusion under different viewing conditions, and analysed the gaze stability of observers viewing the Riley painting and control patterns that do not produce the illusion. Whereas the illusion was reduced, but not abolished, when watching the painting through a pinhole, which reduces the effects of accommodation, it was not perceived in flash afterimages, suggesting an important role for eye movements in generating the illusion for this image. Recordings of eye movements revealed an abundance of small involuntary saccades when looking at the Riley pattern, despite the fact that gaze was kept within the dedicated fixation region. The frequency and particular characteristics of these rapid eye movements can vary considerably between different observers, but, although there was a tendency for gaze stability to deteriorate while viewing a Riley painting, there was no significant difference in saccade frequency between the stimulus and control patterns. Theoretical considerations indicate that such small image displacements can generate patterns of motion signals in a motion-detector network, which may serve as a simple and sufficient, but not necessarily exclusive, explanation for the illusion. Why such image displacements lead to perceptual results with a group of Op Art and similar patterns, but remain invisible for other stimuli, is discussed.