We recorded continuously, with high precision, the positions of the eyes in anesthetized macaque monkeys prepared for physiological recording. Most recordings were made after the infusion of muscle relaxant to immobilize the eyes; in some cases we also were able to record eye position for periods before the eyes were immobilized. In all monkeys, the eyes moved continuously by as much as 0.5 deg over a 10-min sampling period. The average distance moved was proportional to the square root of the sampling period, as would be expected from a random walk. The movements had three distinct components: slow drifts, and two rhythms driven by the pulse and respiration. The rhythmic movements occurred only under paralysis: they were not discernible in measurements made before the infusion of muscle relaxant. The movements of the eye in the paralyzed animal can have substantial effects on the measured physiological characteristics of neurons. For excursions in the midrange of those we observed, a neuron's sensitivity to a spatial frequency of 10 cycle/deg might be underestimated by as much as a factor of three, depending on the method by which responses were averaged. We show how the effects of eye-movements can be mitigated by appropriate data analysis.