When stimuli presented to the two eyes differ considerably, stable binocular fusion fails, and the subjective percept alternates between the two monocular images, a phenomenon known as binocular rivalry. The influence of attention over this perceptual switching has long been studied, and although there is evidence that attention can affect the alternation rate, its role in the overall dynamics of the rivalry process remains unclear. The present study investigated the relationship between the attention paid to the rivalry stimulus, and the dynamics of the perceptual alternations. Specifically, the temporal course of binocular rivalry was studied as the subjects performed difficult nonvisual and visual concurrent tasks, directing their attention away from the rivalry stimulus. Periods of complete perceptual dominance were compared for the attended condition, where the subjects reported perceptual changes, and the unattended condition, where one of the simultaneous tasks was performed. During both the attended and unattended conditions, phases of rivalry dominance were obtained by analyzing the subject"s optokinetic nystagmus recorded by an electrooculogram, where the polarity of the nystagmus served as an objective indicator of the perceived direction of motion. In all cases, the presence of a difficult concurrent task had little or no effect on the statistics of the alternations, as judged by two classic tests of rivalry, although the overall alternation rate showed a small but significant increase with the concurrent task. It is concluded that the statistical patterns of rivalry alternations are not governed by attentional shifts or decision-making on the part of the subject.