The Ternus display produces a bistable illusion of motion: at very short interstimulus intervals (ISIs; < 30 ms) observers perceive element motion while at longer ISIs (> 30 ms) observers perceive group motion. In experiment 1, however, we find that, when the Ternus display's ISI contains an occluding box, group motion is mostly eliminated. These results do not fit the predictions made by the short-range/long-range two-process theory [Braddick and Adlard, 1978, in Visual Psychophysics and Psychology (New York: Academic Press)]. We propose that the differential-activation theory (Gilroy et al, 2001 Perception & Psychophysics63 847–861) accounts for our results. We then extend the differential-activation theory as an explanatory mechanism for the Ternus display in experiment 2 by selectively placing an occluder over the first, second, or third Ternus display element. As predicted by the differential-activation theory, the occlusion of the far-left element produced a normal distribution of group motion increasing with ISI, while the occlusion of the other two elements produced an illusion of occluded elements remaining stationary throughout the display. Furthermore, as predicted by the differential-activation theory, each moving element was assigned to its nearest neighbour, producing, in the case of second and third element occlusion, a novel Ternus display motion illusion where only two out of three elements are perceived as moving.