The functional relationships between the brain areas supposedly involved in the generation of the alpha activity were quantified by means of INTRA- and INTER-hemispheric coherences during different arousal states (relaxed wakefulness, drowsiness at sleep onset, and rapid eye movement sleep) where such an activity can be clearly detectable in the human EEG. A significant decrease in the fronto-occipital as well as in the inter-frontal coherence values in the alpha range was observed with the falling of the vigilance level, which suggests that the brain mechanisms underlying these coherences are state dependent. Making fronto-frontal coherence values in the alpha frequency band useful indexes to discern between brain functional states characterized by a different arousal level.