During non-rapid eye movement (NREM) sleep, neuronal populations in the mammalian forebrain alternate between periods of spiking and inactivity. Termed the slow oscillation in the neocortex and sharp wave-ripples in the hippocampus, these alternations are often considered separately but are both crucial for NREM functions. By directly comparing experimental observations of naturally-sleeping rats with a mean field model of an adapting, recurrent neuronal population, we find that the neocortical alternations reflect a dynamical regime in which a stable active state is interrupted by transient inactive states (slow waves) while the hippocampal alternations reflect a stable inactive state interrupted by transient active states (sharp waves). We propose that during NREM sleep in the rodent, hippocampal and neocortical populations are excitable: each in a stable state from which internal fluctuations or external perturbation can evoke the stereotyped population events that mediate NREM functions.