The interactions between illusory and real contours have been inves- tigated 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 & Dumais, 1975). With line triangles, rivalry is experienced only under dichoptic conditions. A model is proposed to account for the observed phenomena, and the results of simulations are presented.