Adult mammals cycle between periods of sleep and wakefulness. Recent assessments of these cycles in humans and other mammals indicate that sleep bout durations exhibit an exponential distribution, whereas wake bout durations exhibit a power-law distribution. Moreover, it was found that wake bout distributions, but not sleep bout distributions, exhibit scale invariance across mammals of different body sizes. Here we test the generalizability of these findings by examining the distributions of sleep and wake bout durations in infant rats between 2 and 21 days of age. In agreement with Lo et al., we find that sleep bout durations exhibit exponential distributions at all ages examined. In contrast, however, wake bout durations also exhibit exponential distributions at the younger ages, with a clear power-law distribution only emerging at the older ages. Further analyses failed to find substantial evidence either of short- or long-term correlations in the data, thus suggesting that the durations of current sleep and wake bouts evolve through time without memory of the durations of preceding bouts. These findings further support the notion that bouts of sleep and wakefulness are regulated independently. Moreover, in light of recent evidence that developmental changes in sleep and wake bouts can be attributed in part to increasing forebrain influences, these findings suggest the possibility of identifying specific neural circuits that modulate the changing complexity of sleep and wake dynamics during development.