In order to overcome the relatively long delay in processing visual feedback information when pursuing a moving visual target, it is necessary to predict the future trajectory of the target if it is to be tracked with accuracy. Predictive behaviour can be achieved through internal models, and the cerebellum has been implicated as a site for their operation. Purkinje cells in the lateral cerebellum (D zones) respond to visual inputs during visually guided tracking and it has been proposed that their neural activity reflects the operation of an internal model of target motion. Here we provide direct evidence for the existence of such a model in the cerebellum by demonstrating an internal model of a moving external target. Single unit recordings of Purkinje cells in lateral cerebellum (D2 zone) were made in cats trained to perform a predictable visually guided reaching task. For all Purkinje cells that showed tonic simple spike activity during target movement, this tonic activity was maintained during the transient disappearance of the target. Since simple spike activity could not be correlated to eye or limb movements, and the target was familiar and moved in a predictable fashion, we conclude that the Purkinje cell activity reflects the operation of an internal model based on memory of its previous motion. Such a model of the target's motion, reflected in the maintained modulation during the target's absence, could be used in a predictive capacity in the interception of a moving object.