Previous studies have indicated that saccadic eye movements correlate positively with perceptual alternations in binocular rivalry, presumably because the foveal image changes resulting from saccades, rather than the eye movement themselves, cause switches in awareness. Recently, however, we found evidence that retinal image shifts elicit so-called onset rivalry and not percept switches as such. These findings raise the interesting question whether onset rivalry may account for correlations between saccades and percept switches. We therefore studied binocular rivalry when subjects made eye movements across a visual stimulus and compared it with the rivalry in a 'replay' condition in which subjects maintained fixation while the same retinal displacements were reproduced by stimulus displacements on the screen. We used dichoptic random-dot motion stimuli viewed through a stereoscope, and measured eye and eyelid movements with scleral search-coils. Positive correlations between retinal image shifts and perceptual switches were observed for both saccades and stimulus jumps, but only for switches towards the subjects' preferred eye at stimulus onset. A similar asymmetry was observed for blink-induced stimulus interruptions. Moreover, for saccades, amplitude appeared crucial as the positive correlation persisted for small stimulus jumps, but not for small saccades (amplitudes < 1°). These findings corroborate our tenet that saccades elicit a form of onset rivalry, and that rivalry is modulated by extra-retinal eye movement signals.