The log of the amplitude of EEG waves during NREM sleep is a linear function of the log of their frequency. The slope of this function is reliable within individuals, is significantly less steep in elderly than in young subjects and, in both groups, becomes flatter across successive NREM periods. We interpret these results as consistent with the hypothesis that the function of NREM sleep is to reverse the effects of waking on the brain. According to this model the decreased steepness of slope in the elderly and in later NREM periods reflects the diminishing intensity of these processes. Whatever the correct interpretation, the within-subject consistency of slope values permits their empirical study as a function of experimental manipulations. In addition, the quantitative F-A function established here (A = c/Fb) sets constraints that may prove useful for physiologic models of EEG waves during sleep.