When the eyes view incompatible images, binocular rivalry usually results: image constituents in corresponding parts of the monocular visual fields are not perceived simultaneously. We asked naive undergraduates to view dichoptic, dioptic, and monoptic plaids. The dichoptic images evoked strong binocular rivalry when contrast was high, especially if the component gratings were set in motion. Nevertheless, the subjects' visual systems integrated the motion information across the two eyes, producing a unitary motion percept that did not reflect the image in either eye alone. By manipulating the relative spatial scale of the gratings, we affected how well the motion cohered: the results were remarkably similar between dichoptic and traditional dioptic plaids. By manipulating the relative speed of the gratings, we systematically affected the perceived direction of motion of the plaids; these results were also remarkably similar for dichoptic and dioptic plaids. Thus, the motion analysis of dichoptic and dioptic plaids is proceeding according to very similar rules, even though the dichoptic images are incompatible and evoke binocular rivalry.