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Natural environments elicit both phase-locked and non-phase-locked neural responses to the stimulus in the brain. The interpretation of the BOLD signal to date has been based on an association of the non-phase-locked power of high-frequency local field potentials (LFPs), or the related spiking activity in single neurons or groups of neurons. Previous studies have not examined the prediction of the BOLD signal by phase-locked responses. We examined the relationship between the BOLD response and LFPs in the same nine human subjects from multiple corresponding points in the auditory cortex, using amplitude modulated pure tone stimuli of a duration to allow an analysis of phase locking of the sustained time period without contamination from the onset response. The results demonstrate that both phase locking at the modulation frequency and its harmonics, and the oscillatory power in gamma/high-gamma bands are required to predict the BOLD response. Biophysical models of BOLD signal generation in auditory cortex therefore require revision and the incorporation of both phase locking to rhythmic sensory stimuli and power changes in the ensemble neural activity.