The optic tectum of the barn owl contains a map of auditory space. We found that, in response to moving sounds, the locations of receptive fields that make up the map shifted toward the approaching sound. The magnitude of the receptive field shifts increased systematically with increasing stimulus velocity and, therefore, was appropriate to compensate for sensory and motor delays inherent to auditory orienting behavior. Thus, the auditory space map is not static, but shifts adaptively and dynamically in response to stimulus motion. We provide a computational model to account for these results. Because the model derives predictive responses from processes that are known to occur commonly in neural networks, we hypothesize that analogous predictive responses will be found to exist widely in the central nervous system. This hypothesis is consistent with perceptions of stimulus motion in humans for many sensory parameters.