The time course of the different frequency bands in the human sleep EEG spectrum within separate NREM and REM episodes averaged over 24 healthy subjects is measured and plotted with the aim of studying their inter-relationship and also the particularities of the beta band. In NREM, a negative sigma-delta cross-correlation corresponding to that expected from neurophysiological data, is found only in the central zone of each episode. The overall correlation is found to be negligible. A neurophysiological explanation is proposed to account for some aspects of this sigma-delta relation. Below the beta frequency range in NREM, the sequence of build-up in power for the different frequencies is from fast to slow, suggesting that there may be a smooth progression in the frequency of oscillation of the thalamocortical neurons depending on their degree of polarization. The beta band is the only one showing a reciprocal relationship with delta throughout the NREM episode, and it is the only one not declining in the REM episode. These differences, together with the close similarity of the beta evolution with that of the REM-on neuronal activity, suggest that beta could directly reflect this activity.