We have investigated an unusual form of binocular rivalry between two images that are flickered one to each eye, but are never presented simultaneously to the observer. The images were presented in alternation, with a brief dark period between the images. When the flicker frequency was <5 Hz, the subjects primarily experienced a unitary flicker that alternated between the two images. When the flicker frequency was >5 Hz, the subjects primarily experienced two single-image flickers that rival. We investigated magnetoencephalography (MEG) responses at the flicker frequency of the rival stimuli. We found that at some recording locations responses are phase-locked to the flicker that is consciously being perceived. At each flicker rate that induced rivalry, phase shifts following the conscious percept were found consistently at MEG sensors over midline frontal lobe. Most of these sensors show higher magnitude responses when two rivaling flickers are perceived than when a unitary alternating color flicker is perceived. At sensors over occipital lobe, the sensor locations that phase-locked to the perceived flicker depended on the color, orientation, and frequency of flicker. By contrast, sensors over parietal cortex respond preferentially to one flicker, even as the conscious percept changes. Apparently, a large-scale network of cell assemblies in occipital and frontal cortex, responds preferentially to the perceived stimulus during rivalry, and is sensitive to the timing of the flicker driving the conscious percept.