Several mammalian-based theories propose that the varying patterns of neuronal activity occurring in wakefulness and sleep reflect different modes of information processing. Neocortical slow-waves, hippocampal sharp-wave ripples, and thalamocortical spindles occurring during mammalian non-rapid eye-movement (NREM) sleep are proposed to play a role in systems-level memory consolidation. Birds show similar NREM and REM (rapid eye-movement) sleep stages to mammals; however, it is unclear whether all neurophysiological rhythms implicated in mammalian memory consolidation are also present. Moreover, it is unknown whether the propagation of slow-waves described in the mammalian neocortex occurs in the avian "cortex" during natural NREM sleep. We used a 32-channel silicon probe connected to a transmitter to make intracerebral recordings of the visual hyperpallium and thalamus in naturally sleeping pigeons (Columba livia). As in the mammalian neocortex, slow-waves during NREM sleep propagated through the hyperpallium. Propagation primarily occurred in the thalamic input layers of the hyperpallium, regions that also showed the greatest slow-wave activity (SWA). Spindles were not detected in both the visual hyperpallium, including regions receiving thalamic input, and thalamus, using a recording method that readily detects spindles in mammals. Interestingly, during REM sleep fast gamma bursts in the hyperpallium (when present) were restricted to the thalamic input layers. In addition, unlike mice, the decrease in SWA from NREM to REM sleep was the greatest in these layers. Taken together, these variant and invariant neurophysiological aspects of avian and mammalian sleep suggest that there may be associated mechanistic and functional similarities and differences between avian and mammalian sleep.