There is substantial evidence both at the cellular and at the electroencephalogram (EEG) level to support the view that the brainstem activating systems control the sleep-state (stage) progression over time that constitutes the overall sleep structure as seen at the EEG. We argue here that the brainstem therefore modulates the time-courses of spectral power in the different EEG frequency bands. These show during non-rapid eye movement (NREM) sleep a very particular interrelationship the origin of which has received little attention and for which the neuronal transition probability model for sleep structure has proposed a physiological explanation. We advance the hypothesis that if the brainstem is modulating these time-courses then they should show a marked similarity in shape and timing at all sites. Using data from 10 healthy subjects, we measure the degree of similarity of the time-courses over each of the first four NREM episodes at the frontal, central and parietal sites, for each of the frequency bands beta, sigma and delta, and also the cortically generated slow oscillation. All the cross- correlation coefficients are high and statistically significant, indicating that the shape and timing of these time-courses are practically identical at different sites despite regional differences in their average power levels. These results tend to suggest that two processes may operate concurrently: the brainstem controls the shape and timing of the power time-courses while cortical-thalamic interaction controls their site-dependent average power.