Sensorimotor transformation of signals stemming from the visual (eye position) and auditory (binaural information) peripheral organs into a common eye motor error signal was studied; as is observed in the deep layers of the colliculus superior that enables a head fixed monkey to direct its eyes towards an auditory target. By means of a computational model we explore how this transformation can be achieved by the responses of single neurons in the primate brainstem. Our audiooculomotor model, a feed-forward four-layer artificial neural network, was trained with back-propagation of error to assign connectivity in an architecture consistent with known physiology of the primate brainstem at both the level of input, and the output layers. The derived mathematical formalism is consistent with known physiological responses of brainstem neurons and does not require a topographical organization according to their preferred parameter values.