Sleep is observed in most animals, which suggests it subserves a fundamental process associated with adaptive biological functions. However, the evidence to directly associate sleep with a specific function is lacking, in part because sleep is not a single process in many animals. In humans and other mammals, different sleep stages have traditionally been identified using electroencephalograms (EEGs), but such an approach is not feasible in different animals such as insects. Here, we perform long-term multichannel local field potential (LFP) recordings in the brains of behaving flies undergoing spontaneous sleep bouts. We developed protocols to allow for consistent spatial recordings of LFPs across multiple flies, allowing us to compare the LFP activity across awake and sleep periods and further compare the same to induced sleep. Using machine learning, we uncover the existence of distinct temporal stages of sleep and explore the associated spatial and spectral features across the fly brain. Further, we analyze the electrophysiological correlates of micro-behaviours associated with certain sleep stages. We confirm the existence of a distinct sleep stage associated with rhythmic proboscis extensions and show that spectral features of this sleep-related behavior differ significantly from those associated with the same behavior during wakefulness, indicating a dissociation between behavior and the brain states wherein these behaviors reside.