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The central nervous system is a parallel dynamical system which connects sensory input with motor output for the performance of visual tracking. This paper applies elementary control system tools to extend dynamical neural network models to the visual smooth pursuit system. Observed eye position responses to target motions and characteristics of the plant (eye muscles and orbital mechanics) place dynamical constraints on the interposed neural network controller. In the process of constructing a model for the controller, we show two previous pursuit system models, using efference copy and feedforward compensation, are equivalent from an input-output standpoint. We introduce a controller model possessing a potentially highly parallel implementation and offer an example with supporting neural firing rate data. Changes in time delays or other system dynamics are expected to lead to compensatory adaptive changes in the controller. A scheme to noninvasively simulate such changes in system dynamics was developed. Actual physiologic data of adaptive responses to increased time delay is presented as an example of the utility of this parallel controller. Compensatory changes in our parallel controller model are easily predicted. These results suggest a productive interaction between neural network modeling, neurophysiology, and control systems engineering.