Abstract Infra-slow fluctuations (ISFs, 0.008-0.1 Hz) characterize hemodynamic and electric potential signals from the human brain. ISFs are known to correlate with the amplitude dynamics of fast (> 1 Hz) neuronal oscillations, and may arise from permeability fluctuations of the blood-brain barrier (BBB). Slow physiological pulsations such as respiration may also influence the amplitude dynamics of fast oscillations, but it remains uncertain if these processes track the fluctuations of fast cortical oscillations or act as their drivers. Moreover, possible effects of sleep and associated BBB permeability changes on such coupling are unknown. Here, we used non-invasive high-density full-band electroencephalography (EEG) in healthy human volunteers (N=21) to measure concurrently the ISFs, respiratory pulsations, and fast neuronal oscillations during periods of wakefulness and sleep, and to assess the strength and direction of their phase-amplitude coupling. The phases of ISFs and respiration were both coupled with the amplitude of fast neuronal oscillations, with stronger ISF coupling evident during sleep. Causality analysis robustly showed that the phase of ISF and respiration drove the amplitude dynamics of fast oscillations in sleeping and waking states. However, the net direction of modulation was stronger during the awake state, despite the stronger power and phase-amplitude coupling of slow signals during sleep. These findings show that the ISFs in slow cortical potentials and respiration together significantly determine the dynamics of fast cortical oscillations. We propose that these slow physiological phases are involved in coordinating cortical excitability, which is a fundamental aspect of brain function. Significance Statement Previously disregarded EEG infra-slow fluctuations (0.008-0.1 Hz) and slow physiological pulsations such as respiration have been attracting increasing research interest, which shows that both of these signals correlate with fast (> 1 Hz) neuronal oscillations. However, little has been known about the mechanisms underlying these interactions; for example, the direction of causality in this interaction has not hitherto been studied. Therefore, we investigated full-band EEG in healthy volunteers during wakefulness and sleep to determine if ISF and respiration phases drive neuronal amplitudes. Results showed that ISF and respiration are phase-amplitude coupled, and predict neuronal EEG rhythms. Thus, we conclude that fast neuronal rhythms in human brain are modulated by slower non-neural phenomena.