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 oculomotor mechanics encoded in the cerebellum. The cerebellum may also be part of a feedback loop that predicts the displacement of the eyes and compares it to the desired displacement in real time 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 of ipsiversive saccades slowed the deceleration phase. The long latency of these effects and their scaling with light pulse duration are consistent with an integration of neural signals at or downstream of the stimulation site. In contrast, light pulses delivered during contraversive saccades reduced saccade velocity at short latency and were 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 production 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 with optimal peak velocity for the intended displacement.