Evidence for bistability in the perception of motion and stationarity was obtained for a displaced dot-figure embedded in a background of randomly moving noise dots. In the temporal symmetry condition, the figure was presented for the same duration in its two locations; either figure motion or random motion was perceived, depending on the number of noise dots. In the temporal asymmetry condition, the figure was presented for different durations in its two locations; figure motion, a single, stationary figure in a fixed position, or random noise was perceived, again depending on the number of noise dots. Competition between these percepts was established by an analysis of switching rates and by an experiment demonstrating the presence of hysteresis as noise levels were gradually increased and decreased across the figure-motion and figure-stationarity boundaries. This evidence for bistability in the perception of figure motion and figure stationarity (one or the other, but not both, was perceived for the same stimulus) suggested the presence of strong inhibitory competition between motion- and position-detecting mechanisms.