The brain exhibits rich oscillatory dynamics that vary across tasks and states, such as the EEG oscillations that define sleep. These oscillations play critical roles in cognition and arousal, but the brainwide mechanisms underlying them are not yet described. Using simultaneous EEG and fast fMRI in subjects drifting between sleep and wakefulness, we developed a machine learning approach to investigate which brainwide fMRI dynamics predict alpha (8-12 Hz) and delta (1-4 Hz) rhythms. We predicted moment-by-moment EEG power from fMRI activity in held-out subjects, and found that information about alpha power was represented by a remarkably small set of regions, segregated in two distinct networks linked to arousal and visual systems. Conversely, delta rhythms were diffusely represented on a large spatial scale across the cortex. These results identify distributed networks that predict delta and alpha rhythms, and establish a computational framework for investigating fMRI brainwide dynamics underlying EEG oscillations.