In a rapidly changing visual environment, the delay between perception and action might impair the probability of survival of a prey or the efficiency of a predator. In order to compensate for delays associated with sensory-motor processing, primates often make predictions about future events and initiate anticipatory movements. To prepare an anticipatory movement, an estimation of when and where to a target is likely to move is necessary. Such an internal representation is often termed 'expectation'. The aim of this thesis was to investigate the gradual changes of a subject's expectation at the behavioral and electrophysiological levels. Anticipatory smooth pursuit was used in order to study temporal and directional changes in expectation. We found that temporal uncertainty strongly modulated the latency and the velocity of anticipatory movements suggesting that monkeys could estimate the hazard rate of target motion onset in order to decide when to initiate an anticipatory movement. In addition, we have shown that monkeys could use prior directional information in order to voluntarily initiate anticipatory responses in the direction of expected target motion. This prior directional information significantly affected the latency and velocity of these movements. Finally, we have shown that the majority of recorded supplementary eye field (SEF) neurons encoded expected target motion direction. The presence of a directional cue induced an increase of activity in the preferred direction of the neuron. Moreover, a large sub-population of neurons encoded the direction of future anticipatory movement. These results suggest that the SEF could be involved in the cognitive control of anticipatory pursuit eye movements when prior temporal and directional information is provided.