The development of nocturnal sleep and the sleep EEG was investigated in a longitudinal study during infancy. All-night polysomnographic recordings were obtained at home at 2 weeks, and at 2, 4, 6 and 9 months 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, while 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 0.75-25 Hz frequency range. In both QS/NREMS and AS/REMS, EEG power increased with age in the frequency range below 10 Hz and above 17 Hz. The largest rise occurred between 2 and 6 months. A salient feature of the QS/NREMS spectrum was the emergence of a peak in the sigma band (12-14 Hz) at 2 months, which corresponded to the appearance of sleep spindles. Between 2 and 9 months, 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 months, 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 months could be closely approximated by an exponential function. The results suggest that (a) EEG markers of sleep homeostasis appear in the first postnatal months, and (b) sleep homeostasis goes through a period of maturation. Theta activity and not delta activity seems to reflect the dissipation of sleep propensity during infancy.