1. Velocity characteristics of optokinetic nystagmus (OKN) and optokinetic after-nystagmus (OKAN) induced by constant velocity full field rotation were studied in rhesus monkeys. A technique is described for estimating the dominant time constant of slow phase velocity curves and of monotonically changing data. Time constants obtained by this technique were used in formulating a model of the mechanism responsible for producing OKN and OKAN.2. Slow phase velocity of optokinetic nystagmus in response to steps in stimulus velocity was shown to be composed of two components, a rapid rise, followed by a slower rise to a steady-state value. Peak values of OKN slow phase velocity increased linearly with increases in stimulus velocity to 180 degrees /sec. Maximum slow phase eye velocities in the monkey are 2-3 times as great as in humans.3. At the onset of OKAN, slow phase velocity falls by about 10-20%, followed by a slower decline to zero. Peak OKAN slow phase velocities were linearly related to optokinetic stimulus velocities up to 90-120 degrees /sec. Above 120 degrees /sec OKAN slow phase velocity saturated although OKN slow phase velocity continued to increase.4. The charge and discharge characteristics of OKAN were studied. The OKAN mechanism charged in 5-10 sec and discharged over 20-60 sec in darkness. The time constants of decay in OKAN slow phase velocity decreased as stimulus velocities increased. They also decreased on repeated testing. In several monkeys there was a consistent difference in the rate of decay of OKAN slow phase velocity to the right and left.5. Extended visual fixation discharged the activity responsible for producing OKAN. Short fixation times caused only a partial discharge of the OKAN mechanism. Following brief periods of fixation, OKAN resumed but with depressed slow phase velocities.6. A model based on a state realisation of a peak detector was formulated which approximately reproduces the salient characteristics of OKN and OKAN. This model predicts the three dominant characteristics of OKAN: (1) charge over 5-7 sec, (2) slow discharge in darkness, and (3) rapid discharge with visual fixation. With the addition of direct fast forward pathways, it also correctly predicts the rapid and slow rise in OKN. We postulate that OKAN is produced by a central integrator which is also active during OKN. Presumably this integrator acts to maximize velocities during OKN and to smooth and stabilize ocular following during movement of the visual surround.