Categorical perception (CP) is the phenomenon when people are better able to distinguish between stimuli of different categories than between stimuli of the same category and it appears for innate and learned stimuli of various sensory modalities. We tested if CP occurs also for illusory contour stimuli. First, in an ABX paradigm the shape discrimination capacity of subjects was tested for convex (‘fat’) or concave (‘thin’) Kanizsa-square-like shapes (cf Rubin, 1996 Perception25 Supplement, 3; pre-category-learning test). The proportion of correct responses and response latency were measured. Second, subjects were instructed that every stimulus belongs to either the ‘fat’ or the ‘thin’ category, and they were trained to categorise the individual stimuli using a 2AFC paradigm with corrective feedback until 90% of correct responses. Third, we measured the shape discrimination capacity of subjects, by repeating the first ABX paradigm (post-category-learning test). Comparison of the ratio of correct responses in the post/pre discrimination tests showed that discrimination of illusory shapes of different categories is enhanced but discrimination of members of the same category is made more difficult by category training. In a second experiment, by increasing the physical differences between the extreme ‘fat’ and extreme ‘thin’ stimuli (increased range of the opening-angle of the Kanizsa-square inducer pacmen), we made the categorisation task easier for the subjects and tested if discrimination capacity is altered by the modified difficulty of the categorisation task. We discuss the effect of difficulty on CP and the relation of illusory CP to that of real luminance contour stimuli.