The predictive nature of the primate sensorimotor systems, for example the smooth pursuit system and their ability to compensate for long delays have been proven by many physiological experiments. However, few theoretical models have tried to explain these facts comprehensively. Here, we propose a sensorimotor learning and control model that can be used to (1) predict the dynamics of variable time delays and current and future sensory states from delayed sensory information, (2) learn new sensorimotor realities, and (3) control a motor system in real time.