During the transition from neonate to adulthood, brain maturation establishes coherence between behavioral states—wakefulness, non-rapid eye movement, and rapid eye movement sleep. Few studies have characterized and analyzed cerebral rhythms and the sleep–wake cycle in early ages, in relation to adulthood. Since the analysis of sleep in early ages can be used as a predictive model of brain development and the subsequent emergence of neural disturbances in adults, we performed a study on late neonatal and adult wild-type C57BL/6 mice. We acquired longitudinal 24 h electroencephalogram and electromyogram recordings and performed time and spectral analyses. We compared both age groups and found that late neonates: (i) spent moderately more time in wakefulness and less time in non-rapid eye movement sleep, (ii) showed an increased relative band power in delta, which, however, reduced in theta during each behavioral state, (iii) showed a reduced relative band power in beta during wakefulness and non-rapid eye movement sleep, and (iv) manifested an increased total power over all frequencies. Given the mice–human age equivalence, the data presented here might have implications for the clinical context in the analysis of electroencephalogram for sleep-based early and late diagnosis after injury or neurodegeneration.