The brain topography of power spectra along the antero-posterior (A-P) axis was studied in the all-night human sleep EEG. Spectra (0.25 - 25.0 Hz) were computed for an anterior (A; F3-C3), a middle (M; C3-P3) and a posterior (P; P3-O1) bipolar derivation, and the spectral gradients between two adjacent derivations were expressed by power ratios (A/M and M/P). At NREM-REM sleep transitions a power shift from A to M was present over almost the entire frequency range, while the direction of shifts between M and P differed between frequency bands. Within NREM sleep, frequency specific power gradients were present: In the low delta band power in both A (0.25 Hz bin) and P (0.25-1.0 Hz bins) was higher than in M. In the 4-9 Hz range the relation was A > M > P, and in the 15 - 25 Hz range power was largest in M. Power in the spindle frequency range was highest at 11.75 Hz in M, and at 13.5 - 13.75 Hz in A. Topographical differences were seen also in the temporal changes of power across and within NREM sleep episodes. Whereas NREM sleep power in the 2-Hz bin was higher in A than in M in the first episode, this difference vanished in the course of the night. This result points to a specific involvement of frontal parts of the cortex in sleep homeostasis. The regional differences in sleep EEG spectra indicate that sleep is not only a global phenomenon but also a local brain process with a different regional involvement of neuronal populations.