Contrasting hypotheses have been proposed about the functional equivalence between waking saccades and REMs. Patients with left visual hemi-inattention showed dissociation between the direction of waking saccades and that of REMs. REMs directed toward the left were virtually absent, while waking inspective saccades directed in both lateral directions were present, but confined to the right hemispace. It is concluded that: a) the cortical areas regulating attention are relevant in the production of REMs; b) two separate attentional mechanisms have to be considered in relation to the hemi-inattentive syndrome, one is involved in the cognitive control of visual exploration and plays little or no role in the modulation of REMs, the other deals with REMs during sleep and with reflex-like orienting responses to peripheral stimuli during waking.