In addition to modulatory roles concerning bodily functions, sleep is assumed to play a main processing role with regard to newly acquired neural information. Elaboration of memory traces acquired during the waking period is assumed to require two sequential steps taking place during slow wave sleep (SWS) and eventually during paradoxical sleep (PS). This view is suggested by several considerations, not the least of which concerns the natural sequence of appearance of SWS and PS in the adult animal. While the involvement of PS in memory processing is well documented, the involvement of SWS is supported by the results of baseline and post-trial EEG analyses carried out in rats trained for a two-way active avoidance task or a spatial habituation task. Together with control analyses, these data indicate that the marked increase in the average duration of post-trial SWS episodes does not reflect the outcome of non-specific contingent factors, such as sleep loss or stress, but is related to memory processing events. Several considerations have furthermore led to the proposal that, during SWS, after a preliminary selection step, the first processing operation consists in the weakening of non-adaptative memory traces. The remaining memory traces would then be stored again under a better configuration during the ensuing PS episode. This view is in agreement with several relevant features of sleep, including the EEG waveforms prevailing during SWS and PS, as well as the ontogenetic sequence of appearance of SWS and PS. Some theoretical considerations on the role of sleep are also in agreement with the sequential hypothesis. More recent data indicate that the learning capacity of rats is correlated with several baseline EEG features of sleep and wakefulness. They include the average duration of PS episodes and of SWS episodes followed by wakefulness (longer in fast learning rats), and the waking EEG power spectrum of fast learning rats whose output is more balanced in the frequency range below 10 Hz than in slow learning and in non-learning rats. Additional EEG data suggest that fast learning rats may accomplish 'on line' processing of newly acquired information according to a sequence of events not dissimilar from the one proposed by the sequential hypothesis.