The relation between the duration of prior wakefulness and EEG power density during sleep in humans was assessed by means of a study of naps. The duration of prior wakefulness was varied from 2 to 20 hr by scheduling naps at 1000 hr, 1200 hr, 1400 hr, 1600 hr, 1800 hr, 2000 hr, and 0400 hr. In contrast to sleep latencies, which exhibited a minimum in the afternoon, EEG power densities in the delta and theta frequencies were a monotonic function of the duration of prior wakefulness. The data support the hypothesis that EEG power density during non-rapid eye movement sleep is only determined by the prior history of sleep and wakefulness and is not determined by clock-like mechanisms.