Faint tones were presented at intervals (average 16 s) throughout a night's sleep; whenever they heard them, subjects pressed a palm-mounted button to switch them off. At the same time, electroencephalogram (EEG) was recorded. Button-press responses occurred in all EEG stages of sleep except Stage 4, although there was only one behavioral response (BR) in Stage 3 and one in REM. The mean probability of response (PR)/Stage was Stage 1 = 0.235, Stage 2 = 0.016, Stage 3 = 0.001, Stage 4 = 0.000, Stage REM = 0.0004. Also, responses sometimes failed to occur in EEG Stage wake (PR = 0.94), particularly near sleep onset. If the criterion for wakefulness is cognitive response to external stimulation, only in EEG Stages 3, 4, and REM can accurate distinctions between sleep and wakefulness be made. If EEG is the criterion, then the data suggest that cognitive response is possible during Stages 1 and 2 "sleep." The concept of a sleep onset period (SOP), characterized by lengthening response times and intermittent response failure (thereby reflecting neither true sleep or wakefulness), may provide a useful resolution of this definitional dilemma.