1. Thresholds for discrimination of orientation were measured for solid and interrupted lines, and for illusory borders defined by offset abutting lines of a variety of configurations. 2. Illusory contours defined by orthogonal lines with a clear gap or overlap manifest excellent orientation discrimination even for very short exposure durations, and are robust to pattern motion and masking. The performance is almost as good as that for real lines. 3. When the contour is made up of abutting lines without gap or overlap, orientation discrimination is not nearly as good, and deteriorates further with short exposure duration, with target motion, and with masking. 4. The introduction of disparity in such illusory borders does not improve the discrimination of its orientation, so that concepts such as surface elaborations do not yet have to be invoked. 5. The results suggest that there is one class of illusory contour whose orientations can be discriminated by virtue of its delivering adequate stimuli to orientation-selective units in primary visual cortex. For contours with a uniform space-averaged luminance, the orientation discrimination is helped by the orthogonality of the generating lines, and this gives support to the concept that orthogonally oriented end-stopped neurons may participate in the orientation discrimination.