The aim of the study was to determine whether accommodation to the relative motion of a target along the visual axis of one eye during fore-aft movement of the head could induce accurate vergence over a wide range of viewing distances and frequencies of oscillation, despite lack of vision in the second eye. This was compared to the vergence when both eyes viewed the target. Two rhesus monkeys were trained to fixate a visual target located 216-336 mm in front and along the visual axis of one eye, while being sinusoidally translated in the fore-aft direction. There was no movement of the seeing eye while the other eye converged, regardless of whether there was vision in the converged eye. Gain and phase of the convergence were determined based on the ratio of actual versus expected eye position if the target was accurately fixated. During translation at frequencies from 0.05 to 2 Hz, the eye converged on the target with an eye position gain of approximately 1, and a phase close to zero. When vision was occluded in the converging eye, gains of convergence were 0.6-0.8 Hz up to 2 Hz, and the phases remained close to zero. At low frequencies of fore-aft movement, when the acceleration was negligible, convergence was driven by accommodation in the seeing eye. At higher frequencies, vergence could also be driven by the linear vestibulo-ocular reflex (lVOR). Thus, vision in one nonmoving eye and the lVOR combine to generate convergence over a wide range of frequencies and viewing distances.