Internal models are essential for the production of accurate movements. The accuracy of saccadic eye movements is thought to be mediated by an internal model of orbital mechanics encoded in the cerebellum. The cerebellum may also be part of a feedback loop that predicts the displacement of the eye in real time and compares the predicted displacement to the desired displacement command to ensure that saccades land on target. To investigate the role of the cerebellum in these two aspects of saccade production, we delivered saccade-triggered light pulses to channelrhodopsin-2-expressing Purkinje cells in the oculomotor vermis (OMV) of two macaque monkeys. Light pulses delivered during the acceleration phase slowed the deceleration phase of ipsiversive saccades. The long latency of these effects, and their scaling with light pulse duration, are consistent with an integration of neural signals downstream of the stimulation. In contrast, light pulses delivered during contraversive saccades reduced saccade velocity at a short latency (~6 ms) that was followed by a compensatory reacceleration which caused gaze to land near or on the target. We conclude that the contribution of the OMV to saccade control depends on saccade direction; the ipsilateral OMV is part of a forward model that predicts eye displacement, whereas the contralateral OMV is part of an inverse model that creates the force required to move the eyes accurately.