We report that some well known geometrical illusions disappear when the eyes are fixating and saccades are suppressed for some period of time. The disappearance is not accompanied by fading due to stabilisation of the retinal image. Any saccade made on purpose restored the illusion immediately. The fixation time after which some illusions disappeared was measured for 4 illusions and 4 subjects each. Effects of practice are observed after repetition of the measurement day after day. We suggest that present theories of vision cannot readily explain the effect.