Eye position and angular velocity were measured in squirrel monkeys (Saimiri sciureus) by means of the electromagnetic scleral search-coil technique. Horizontal sigma-optokinetic nystagmus (sigma-OKN) was elicited by a stationary, stroboscopically illuminated, periodic, vertical-stripe pattern lining a vertical cylinder. The relationship between the mean slow-phase eye angular velocity, Ve, of sigma-OKN and the product of pattern period, Ps, and flash frequency, f(s), was determined. When Ve approximated k x Ps x f(s) (deg x s(-1)) and k was an integer > or = 1, the sigma-paradigm was fulfilled. Sigma-OKN could be evoked in different "modes", whereby k approximated 1, 2,...n. The sigma-OKN properties of squirrel monkeys were similar to those measured for sigma-OKN in the "stare" mode in man, with the exception of a long-lasting optokinetic afternystagmus (sigma-OKAN) appearing in the monkey. A considerable amount of temporal variability in flash sequence intervals ("temporal noise"), causing retinal error signals that interfered with the sigma-paradigm, was accepted by the visuo-motor system without interruption of sigma-OKN. This observation was explained by the operation of a short memory device for perception of visual motion. The internal gain, g(i), which relates the retinal "error" displacement velocity, Vr, and Ve depended, in turn, on Vr according to a function resembling the known relationship between neuronal activity of NOT (nucleus of the optic tract) nerve cells and Vr. This observation may be taken as direct proof that sigma-OKN can be explained by a centrally preprogrammed relationship between the retinal velocity, Vr, and the OKN slow-phase eye velocity, Ve. It is stipulated that the sum of Vr and efference copy signals generated in cortical or subcortical gaze centers is the essential component controlling the perceived velocity of the sigma-movement, whereby a short-term integrator plays a role for squirrel monkey sigma-OKN. When the flash frequency, f(s), was modulated periodically according to a sinewave or "triangular" function at a rate below 0.5 cycles x s(-1), Ve was found to respond with a corresponding modulation, provided the modulation amplitude did not exceed 50% of the mean flash rate. When the latter occurred, nonlinear responses could be observed. A similar response was found when the speed of "real" optokinetic stimuli was varied sinusoidally. Under these experimental conditions, however, the amplitude of the Ve variation yielded up to 1.0 approximately linear responses.