Rapid eye movement (REM) sleep is often considered to be a global brain state. Here, electroencephalogram recordings during human REM sleep revealed two independent, spatially separate clusters of slow, delta-frequency waves: fronto-central ‘sawtooth’ waves that occurred during eye movements, and slower medial-occipital waves, similar to those seen during non-REM sleep. Thus, delta waves are a feature of REM sleep, and REM sleep is a spatiotemporally heterogeneous brain state.