The development of nocturnal sleep and the sleep electroencephalogram (EEG) was investigated in a longitudinal study during infancy. All-night polysomnographic recordings were obtained at home at 2 wk and at 2, 4, 6, and 9 mo after birth (analysis of 7 infants). Total sleep time and the percentage of quiet sleep or non-rapid eye movement sleep (QS/NREMS) increased with age, whereas the percentage of active sleep or rapid eye movement sleep (AS/REMS) decreased. Spectral power of the sleep EEG was higher in QS/NREMS than in AS/REMS over a large part of the 0.75- to 25-Hz frequency range. In both QS/NREMS and AS/REMS, EEG power increased with age in the frequency range <10 Hz and >17 Hz. The largest rise occurred between 2 and 6 mo. A salient feature of the QS/NREMS spectrum was the emergence of a peak in the sigma band (12-14 Hz) at 2 mo that corresponded to the appearance of sleep spindles. Between 2 and 9 mo, low-frequency delta activity (0.75-1.75 Hz) showed an alternating pattern with a high level occurring in every other QS/NREMS episode. At 6 mo, sigma activity showed a similar pattern. In contrast, theta activity (6.5-9 Hz) exhibited a monotonic decline over consecutive QS/NREMS episodes, a trend that at 9 mo could be closely approximated by an exponential function. The results suggest that 1) EEG markers of sleep homeostasis appear in the first postnatal months, and 2) sleep homeostasis goes through a period of maturation. Theta activity and not delta activity seems to reflect the dissipation of sleep propensity during infancy.