The antisaccade task is a model of the conflict between an unwanted reflexive response (which must be inhibited) and an appropriate volitional response (which must be generated). In this talk I will present a study of the neural correlates of these cognitive components separately using a delayed saccade paradigm to dissociate saccade inhibition from generation. Event-related functional magnetic resonance imaging (fMRI) was carried out in healthy human volunteers. It was found that the right supramarginal gyrus showed significantly greater activation during response inhibition compared to response generation, suggesting a role in saccade inhibition or stimulus detection. The right lateral frontal eye field and bilateral intraparietal sulcus showed evidence of selective involvement in antisaccade generation. Ventrolateral and dorsolateral prefrontal cortices showed comparable levels of activation in both phases of the task. These areas likely fulfil a more general supervisory role in the volitional control of eye movements, such as stimulus appraisal, task set, and decision making. The findings will be discussed in relation to data suggesting that antisaccade deficits constitute an endophenotype for schizophrenia and in relation to pharmacological studies of brain function during antisaccade eye movements.