Neurophysiological studies have shown that the deeper layers of the superior colliculus (SC) contain a topographical neural map representing the ocular vectorial displacement required for foveation of the target (motor error). It is known that the location of the active area in this neural map can be updated, not only following changes in retinal error, but also by efference-copy signals representing a change in eye position. Since it can be shown that a two-layer feedforward network cannot perform this task, we have simulated this system by training a three-layered neural network with access to retinal error and efference copy information about eye position. The network was taught to code motor error topographically (as in the collicular motor map) by generating population activity at the appropriate location in its output layer for different combinations of visual and efference copy signals. After the network had learned the required remapping transformation with sufficient precision (error of one deg over an 80 x 80 deg working range), the properties of the trained network were analyzed. From an investigation of the activity patterns of the hidden units in the trained network it appeared that information about target location relative to the head, implicitly present at the level of input signals, is no longer available at the level of the hidden layer. More detailed inspection of the properties of these units revealed that they code motor error. Their movement field is a monotonic function of motor error amplitude, and shows broad direction tuning specific for each unit. Finally, simulations were made with a four layered network with an architecture and access to input signals closely mimicking Robinson's model of the saccadic system. Again, the network was trained to represent motor error topographically in its output layer. The model shows, for the first time, how the computation of the topographical motor error map in the SC from retinal and eye position signals may proceed in two steps, involving a stage where target location is coded in a distributed fashion in craniotopic coordinates and a subsequent supracollicular stage, where radial motor error is represented in a firing-rate code in units with broad tuning characteristics. These two stages in the model show interesting similarities with the characteristics of neuron populations shown neurophysiologically in area 7a and parietal region LIP, respectively.