Frontal-eyed primates use both smooth pursuit in frontoparallel planes (frontal pursuit) and pursuit-in-depth (vergence pursuit) to track objects moving slowly in 3-dimensional (3D) space. To understand how 3D-pursuit signals represented in frontal eye fields are processed further by downstream pathways, monkeys were trained to pursue a spot moving in 3D virtual space. We characterized pursuit signals in Purkinje (P) cells in the cerebellar dorsal vermis and their discharge during vergence pursuit. In 41% of pursuit P-cells, 3D-pursuit signals were observed. However, the majority of vermal-pursuit P-cells (59%) discharged either for vergence pursuit (43%) or for frontal pursuit (16%). Moreover, the majority (74%) of vergence-related P-cells carried convergence signals, displaying both vergence eye position and velocity sensitivity during sinusoidal and step vergence eye movements. Preferred frontal-pursuit directions of vergence + frontal-pursuit P-cells were distributed in all directions. Most pursuit P-cells (73%) discharged before the onset of vergence eye movements; the median lead time was 16 ms. Muscimol infusion into the sites where convergence P-cells were recorded resulted in a reduction of peak convergence eye velocity, of initial convergence eye acceleration, and of frontal-pursuit eye velocity. These results suggest involvement of the dorsal vermis in conversion of 3D-pursuit signals and in convergence eye movements.