Although the extrapolation of past perceptual history into the immediate and distant future is a fundamental phenomenon in everyday life, the underlying processing mechanisms are not well understood. A network model consisting of interacting excitatory and inhibitory cell populations coding for stimulus position is used to study the neuronal population response to a continuously moving stimulus. An adaptation mechanism is proposed that offers the possibility to control and modulate motion-induced extrapolation without changing the spatial interaction structure within the network. Using an occluder paradigm, functional advantages of an internally generated model of a moving stimulus are discussed. It is shown that the integration of such a model in processing leads to a faster and more reliable recognition of the input stream and allows for object permanence following occlusion. The modeling results are discussed in relation to recent experimental findings that show motion-induced extrapolation.