While viewing an unambiguously rotating circular array of bars for an extended period, most perceive the array to occasionally move in the direction opposite to its true motion. We find that this alternation in perception has similar dynamics to rivalry, including little correlation among the durations of successive percepts. We also describe analogous reversals in touch and in proprioception. In the proprioceptive case, biceps vibration induces illusory forearm extension. Occasionally, although the same stimulation continues, reversals occur-flexion is perceived rather than extension. Temporal sampling is often invoked to explain the visual reversals but it cannot explain these proprioceptive reversals. Instead, after initial adaptation to the stimulus, rivalry between signals indicating the opposing directions could potentially explain reversals in all three modalities.