Saccadic accuracy requires that the control signal sent to the motor neurons must be the right size to bring the fovea to the target, whatever the initial position of the eyes (and corresponding state of the eye muscles). Clinical and experimental evidence indicates that the basic machinery for generating saccadic eye movements, located in the brainstem, is not accurate: learning to make accurate saccades requires cerebellar circuitry located in the posterior vermis and fastigial nucleus. How do these two circuits interact to achieve adaptive control of saccades? A model of this interaction is described, based on Kawato's principle of feedback-error-learning. Its three components were (1) a simple controller with no knowledge of initial eye position, corresponding to the superior colliculus; (2) Robinson's internal feedback model of the saccadic burst generator, corresponding to preoculomotor areas in the brain-stem; and (3) Albus's Cerebellar Model Arithmetic Computer (CMK), a neural net model of the cerebellum. The connections between these components were (I) the simple feedback controller passed a (usually inaccurate) command to the pulse generator, and (2) a copy of this command to the CMAC; (3) the CMAC combined the copy with information about initial eye position to (4) alter the gain on the pulse generator's internal feedback loop, thereby adjusting the size of burst sent to the motor neurons. (5) If the saccade were inaccurate, an error signal from the feedback controller adjusted the weights in the CMAC. It was proposed that connection (2) corresponds to the mossy fiber projection from superior colliculus to oculomotor vermis via the nucleus reticularis tegmenti pontis, and connection (5) to the climbing fiber projection from superior colliculus to the oculomotor vermis via the inferior olive. Plausible initialization values were chosen so that the system produced hypometric saccades (as do human infants) at the start of learning, and position-dependent hypermetric saccades when the cerebellum was removed. Simulations for horizontal eye movements showed that accurate saccades from any starting position could be learned rapidly, even if the error signal conveyed only whether the initial saccade were too large or too small. In subsequent tests the model adapted realistically both to simulated weakening of the eye muscles, and to intrasaccadic displacement of the target, thereby mimicking saccadic plasticity in adults. The architecture of the model may therefore offer a functional explanation of hitherto mysterious tectocerebellar projections, and a framework for investigating in greater detail how the cerebellum adaptively controls saccadic accuracy.