Since most gaze shifts are to targets that lie at a different distance from the viewer than the current target, gaze changes commonly require a change in the angle between the eyes. As part of this response, lens curvature must also be adjusted with respect to target distance by the ciliary muscle. It has been suggested that projections by the cerebellar fastigial and posterior interposed nuclei to the supraoculomotor area (SOA), which lies immediately dorsal to the oculomotor nucleus and contains near response neurons, support this behavior. However, the SOA also contains motoneurons that supply multiply innervated muscle fibers (MIFs) and the dendrites of levator palpebrae superioris motoneurons. To better determine the targets of the fastigial nucleus in the SOA, we placed an anterograde tracer into this cerebellar nucleus in Macaca fascicularis monkeys and a retrograde tracer into their contralateral medial rectus, superior rectus, and levator palpebrae muscles. We only observed close associations between anterogradely labeled boutons and the dendrites of medial rectus MIF and levator palpebrae motoneurons. However, relatively few of these associations were present, suggesting these are not the main cerebellar targets. In contrast, labeled boutons in SOA, and in the adjacent central mesencephalic reticular formation (cMRF), densely innervated a subpopulation of neurons. Based on their location, these cells may represent premotor near response neurons that supply medial rectus and preganglionic Edinger–Westphal motoneurons. We also identified lens accommodation-related cerebellar afferent neurons via retrograde trans-synaptic transport of the N2c rabies virus from the ciliary muscle. They were found bilaterally in the fastigial and posterior interposed nuclei, in a distribution which mirrored that of neurons retrogradely labeled from the SOA and cMRF. Our results suggest these cerebellar neurons coordinate elements of the near response during symmetric vergence and disjunctive saccades by targeting cMRF and SOA premotor neurons.