How general anesthetics cause loss of consciousness is unknown. Some evidence points toward effects on the neocortex causing “top-down” inhibition, whereas other findings suggest that these drugs act via subcortical mechanisms, possibly selectively stimulating networks promoting natural sleep. To determine whether some neuronal circuits are affected before others, we used Morlet wavelet analysis to obtain high temporal resolution in the time-varying power spectra of local field potentials recorded simultaneously in discrete brain regions at natural sleep onset and during anesthetic-induced loss of righting reflex in rats. Although we observed changes in the local field potentials that were anesthetic-specific, there were some common changes in high-frequency (20–40 Hz) oscillations (reductions in frequency and increases in power) that could be detected at, or before, sleep onset and anesthetic-induced loss of righting reflex. For propofol and natural sleep, these changes occur first in the thalamus before changes could be detected in the neocortex. With dexmedetomidine, the changes occurred simultaneously in the thalamus and neocortex. In addition, the phase relationships between the low-frequency (1–4 Hz) oscillations in thalamic nuclei and neocortical areas are essentially the same for natural sleep and following dexmedetomidine administration, but a sudden change in phase, attributable to an effect in the central medial thalamus, occurs at the point of dexmedetomidine loss of righting reflex. Our data are consistent with the central medial thalamus acting as a key hub through which general anesthesia and natural sleep are initiated.