1. The aim of this paper is to present a new hypothesis to explain the evolution of the sleeping and waking states. 2. We propose that the reptilian waking state and the mammalian slow wave sleep are homologous states. 3. We also propose that instead of looking at the polygraphic sleep as a new evolutive acquisition of mammals and birds, it seems more convenient to look at the full waking state; the "advanced wakefulness" as the true new evolutionary acquisition of these animals. 4. These conclusions are reached after examining some available reports of slow wave electroencephalogram in waking reptiles, some other reports showing signs of rapid eye movement sleep in this same group and the coevolution between sleep states and thermoregulation. Finally, a clear parallelism between sleep ontogeny and phylogeny is shown under the light of the proposed hypothesis.