During the last 30 years, paradoxical sleep (PS) has been generally considered as the only type of sleep involved in memory processing, mainly for the consistent increase of PS episodes in laboratory animals learning a relatively complex task, and for the retention deficits induced by post-training PS deprivation. The vicissitudes of this idea, examined in detail by several laboratories, have been critically presented in a number of review articles However, according to a more comprehensive unitary proposal (the sequential hypothesis), memory processing during sleep does require the initial participation of slow-wave sleep (SS) in addition to the subsequent involvement of PS. The evidence supporting this hypothesis, largely derived from experiments concerning rats trained for a two-way active avoidance task, is reviewed here in some detail. Recent studies of human sleep are in full agreement with this view. In the rat, the main effect of learning on post-training SS consists in the selective increment in the average duration of SS episodes initiating different types of sleep sequences. Notably, following training for a two-way active avoidance task, the occurrence of this effect in sleep sequences including transition sleep (TS), such as SS→TS→W and SS→TS→PS, appears related to the processing of memories of the novel avoidance response. Conversely, the occurrence of the same effect in sleep sequences lacking TS may reflect the processing of memories of innate responses (escapes and freezings). Memories of innate and novel responses are assumed to engage in a dynamic competitive interaction to attain control of waking behaviour. Interestingly, in baseline sleep, variables of SS→TS→W and SS→TS→PS sequences, such as the average duration of SS, TS, and PS episodes, have proved to be good indices of the capacity to learn, as shown by their strong correlations with the number of avoidances scored by rats the following day. Comparable correlations have not been displayed by variables of baseline SS→W and SS→PS sequences.