Many different anesthetics cause loss of responsiveness despite having diverse underlying molecular and circuit actions. To explore the convergent effects of these drugs, we examined how ketamine, an N-methyl-D-aspartate (NMDA) receptor antagonist, and dexmedetomidine, an α2 adrenergic receptor agonist, affected neural oscillations in the prefrontal cortex of nonhuman primates. Previous work has shown that anesthesia increases phase locking of low-frequency local field potential activity across cortex. We observed similar increases with anesthetic doses of ketamine and dexmedetomidine in the ventrolateral and dorsolateral prefrontal cortex, within and across hemispheres. However, the nature of the phase locking varied between regions. We found that oscillatory activity in different prefrontal subregions within each hemisphere became more anti-phase with both drugs. Local analyses within a region suggested that this finding could be explained by broad cortical distance-based effects, such as a large traveling wave. By contrast, homologous areas across hemispheres increased their phase alignment. Our results suggest that the drugs induce strong patterns of cortical phase alignment that are markedly different from those in the awake state, and that these patterns may be a common feature driving loss of responsiveness from different anesthetic drugs.