We consider the problem of sensorimotor delays in the optimal control of movement under un- certainty. Specifically, we consider axonal conduction delays in the visuo-oculomotor loop and their implications for active inference. Active inference uses a generalisation of Kalman filter- ing to provide Bayes optimal estimates of hidden states and action in generalised coordinates of motion. Representing hidden states in generalised coordinates provides a simple means of compensating for both sensory and oculomotor delays. This compensation is illustrated us- ing neuronal simulations of oculomotor following responses with and without compensation. We then consider an extension of the generative model that produces ocular following to simulate smooth pursuit eye movements — in which the system believes both the target and its centre of gaze are attracted by a (fictive) point moving in the visual field. Finally, the gen- erative model is equipped with a hierarchical structure, so that it can register and remember unseen (occluded) trajectories and emit anticipatory responses. These simulations speak to a straightforward and neurobiologically plausible solution to the generic problem of integrating information from different sources with different temporal delays and the particular difficulties encountered when a system — like the oculomotor system — tries to control its environment with delayed signals.