Recordings from neurons in the vestibular nuclei indicate that the cells that carry eye position signals encode the position of a single eye (either ipsilateral or contralateral) during both conjugate and vergence eye movements. The fact that the vestibular nuclei are aware of the positions of each eye is not surprising as the otolith-based linear vestibulo-ocular reflex is known to change its behaviour as a function of uniocular eye position. This result suggests that the signal coming from the oculomotor velocity-to-position integrator specifies the position of each eye during vergence movements and thus must receive a vergence velocity input along with its conjugate velocity inputs. As there is no vergence system in laterally eyed animals, we have proposed two possible models of integrator arrangement that could have developed from conjugate directional (rather than uniocular) integrators in lower animals without frontally mounted eyes. Both of these models explain the existence of near-response cells and produce the required bidirectional gaze paretic nystagmus following unilateral lesions of one integrator. The models also make specific and different predictions concerning the effects of unilateral integrator lesions on the behaviour of the vergence system and thus make suggestions for further experiments.