The possible role of the cerebellum for the control of saccades and gaze holding is reconsidered using a computational modeling approach. As suggested by previous research, control of gaze holding is assumed to be enhanced by the floccular lobe, whereas control of the saccadic pulse is governed by the oculomotor vermis and fastigial nucleus. In the present work, a negative feedback loop via the paramedian tract neurons and the floccular lobe that contains a forward model of the oculomotor plant is supposed to enhance the time constant of the brainstem integrator. Control of saccadic amplitude is hypothesized to be achieved by a more complex network: feedforward projections from the superior colliculus via the nucleus reticularis tegmenti pontis to the oculomotor vermis and fastigial nucleus cooperate with feedback connections from excitatory burst neurons to overcome the sluggishness of the assumed local feedback loop formed via the superior colliculus and to implement inverse dynamics of downstream neural and motor processing.