Efficient executive control frequently requires the timely activation or re-activation of a task-goal to enable purposeful behaviour. Additionally, more generalized factors such as alertness or neurological health will influence the efficiency with which control can be implemented. Goal-directed processes have been investigated by examining event-related potentials (ERPs), but much less is known about the involvement of background or 'tonic' processes reflected in the ongoing electroencephalogram (EEG), and how these affect the phasic processes expressed in the broad-band ERP. Here, we investigate the relationship between a key attention-sensitive tonic process--the alpha rhythm--and relevant phasic processes observed during a sustained attention paradigm in neurologically healthy subjects. We report that subjects with relatively higher tonic alpha power (approximately 10 Hz) show a larger-amplitude late positive ERP component that is thought to index goal activation and has been found to predict good sustained attention performance as defined by correct response patterns. Source localization results suggest that the neural generators responsible for oscillatory alpha activity, which are found primarily in the parietal and occipital lobes, are distinct from those giving rise to the late positive component. The results are discussed in terms of increased alpha synchrony facilitating goal-directed behaviour.