The interactions between illusory and real contours have been investigated under monocular, binocular and dichoptic conditions. Results show that under all three presentation conditions, periodic alternations, generally called rivalry, occur during the perception of cognitive (or illusory) triangles, while earlier research had failed to find such rivalry (Bradley and Dumais 1975). With line triangles, rivalry is experienced only under dichoptic conditions. A model is proposed to account for the observed phenomena.