We conducted behavioral and EEG experiments to identify physiological correlates of perceptual binding during two types of binocular rivalry: (1) conventional 'eye' rivalry where perception alternates between the two monocular images presented one to each eye and (2) interocular 'percept' rivalry, where perception alternates between percepts formed by grouping complementary hemifields one from each eye. We employed 'frequency-tagging' by flickering a grating in each hemifield of each eye at different frequencies to elicit SSVEP responses specific to each hemifield of each eye. When the gratings in complementary visual fields of the two eyes were congruent in color and orientation, robust interocular 'percept' rivalry was observed with roughly equal probability to conventional 'eye' rivalry. The SSVEPs evoked by the flickering gratings were enhanced by conscious perception at both posterior and frontal electrodes only during conventional 'eye' rivalry and not during interocular 'percept' rivalry, suggesting that dominance of one eye is the basis of most previous reports of SSVEP modulation by conscious perception. We also observed nonlinear SSVEP responses at the sums of our four fundamental frequencies. These combination responses were only produced by flicker in complementary visual hemifields--in the same eye or across eyes, but never by incongruent flickering gratings that occupy the same visual field across eyes, suggesting that they are related to the binding of the visual hemifields (monocular or interocular) into a coherent percept. These combination responses were modulated by the type of rivalry experienced by the observer, but not by the specific conscious perception. Neural processes related to perceptual binding of both rival percepts take place during binocular rivalry even when only one percept is consciously perceived. This suggests that conventional 'eye' and interocular 'percept' rivalry both involve competition between percepts.