In normal vision, the inputs from the two eyes are integrated into a single percept. When dissimilar images are presented to the two eyes, however, they compete for perceptual dominance, so that one eye's view suppresses that of the other. Recent evidence suggests that this phenomenon, known as binocular rivalry, arises through competition between alternative stimulus interpretations in extrastriate cortex. Because eye-specific information appears to be lost at this stage, it remains unclear how the stimulus conditions that yield binocular rivalry are distinguished from those that produce stable single vision. Using a neural network that models the mammalian early visual system, I investigate here the hypothesis that congruent and conflicting stimuli are distinguished by their different effects on the relative timing of action potentials in primary visual cortex (V1), where monocular inputs are first combined. In the model, congruent stimulation of both eyes results in synchronization of discharges among binocular neurons in V1. By contrast, conflicting stimulation of the two eyes results in neuronal asynchrony in this area. This asynchrony then produces rivalrous response suppression at later stages in the visual pathway. Synchronization of firing in V1, however, prevents such competition, thereby ensuring non-rivalrous responses. These novel effects of spike timing on competition emerge naturally from the network dynamics. The results suggest that input-related differences in relative spike timing at an early stage of visual processing may play an important part in the phenomena both of binocular integration and rivalry; furthermore, they indicate that the temporal patterning of cortical activity may be a fundamental mechanism of selection among competing stimulus representations.