Certain premotor neurons of the oculomotor system fire at a rate proportional to desired eye velocity. Their output is integrated by a network of neurons to supply an eye positon command to the motoneurons of the extraocular muscles. This network, known as the neural integrator, is calibrated during infancy and then maintained through development and trauma with remarkable precision. We have modeled this system with a self-organizing neural network that learns to integrate vestibular velocity commands to generate appropriate eye movements. It learns by using current eye movement on any given trial to calculate the amount of retinal image slip and this is used as the error signal. The synaptic weights are then changed using a straightforward algorithm that is independent of the network configuration and does not necessitate backwards propagation of information. Minimization of the error in this fashion causes the network to develop multiple positive feedback loops that enable it to integrate a push-pull signal without integrating the background rate on which it rides. The network is also capable of recovering from various lesions and of generating more complicated signals to simulate induced postsaccadic drift and compensation for eye muscle mechanics.