All-night sleep electroencephalograms were recorded in healthy adults in order to perform spectral analysis in different sleep stages. From each subject 13 EEG samples of 40 sec length were selected from the various sleep stages for computation of variance or power spectra, coherence and phase spectra. Variance spectra display the spectral distribution of the average intensity (mean square value or variance) of the different frequency components. They allowed an exact quantification of the background activity in the different sleep stages, especially regarding frequency and intensity of peaks in the δ-, α-, σ- and β-band. The results showed that σ -activity (activity in the frequency band of sleep spindles) is an obligatory component of sleep stages C, D and E, is facultative in the intermediate phase and may occur also during paradoxical sleep. Variance spectra seem to have only limited application for automatic scoring of sleep stages when using the conventional classification schemes of Loomis or of Dement and Kleitman, Coherence spectra provide a measure of correlation between two simultaneous EEG records as a function of frequency. Between bilateral homologous derivations high coherence was found for all frequencies between 0.25 and 20–40 Hz in all stages of slow-wave sleep as well as in paradoxical sleep. Between anterior and posterior derivations significant coherence was essentially restricted to the σ -band. These findings indicate the presence of a common source for σ -activity, probably located in the anterior thalamic nuclei. In contrast to σ -activity the other frequency components, especially δ -activity, show only bilateral phase-locking and, therefore, are generated by more than one source.