Neural suppression plays an important role in cortical function, including sensory, memory, and motor systems. It remains, however, relatively poorly understood. A paradigmatic case arises when conflicting images are presented to the two eyes. These images can compete for awareness, and one is usually strongly suppressed. The mechanisms that resolve such interocular conflict remain unclear. Suppression could arise solely from "winner-take-all" competition between neurons responsive to each eye. Alternatively, suppression could also depend upon neurons detecting interocular conflict. Here, we provide physiological evidence in human visual cortex for the latter: suppression depends upon conflict-sensitive neurons. We recorded steady-state visual evoked potentials (SSVEP), and used the logic of selective adaptation. The amplitude of SSVEP responses at intermodulation frequencies strengthened as interocular conflict in the stimulus increased, suggesting the presence of neurons responsive to conflict. Critically, adaptation to conflict both reduced this SSVEP effect, and increased the amount of conflict needed to produce perceptual suppression. The simplest account of these results is that interocular-conflict-sensitive neurons exist in human cortex: adaptation likely reduced the responsiveness of these neurons which in turn raised the amount of conflict required to produce perceptual suppression. Similar mechanisms may be used to resolve other varieties of perceptual conflict.