Brief stimuli presented near the onset of saccades are grossly mislocalized in space. In this study, we investigated whether the Bayesian hypothesis of optimal sensory fusion could account for the mislocalization. We required subjects to localize visual, auditory, and audiovisual stimuli at the time of saccades ( compared with an earlier presented target). During fixation, vision dominates and spatially "captures" the auditory stimulus (the ventriloquist effect). But for perisaccadic presentations, auditory localization becomes more important, so the mislocalized visual stimulus is seen closer to its veridical position. The precision of the bimodal localization ( as measured by localization thresholds or just-noticeable difference) was better than either the visual or acoustic stimulus presented in isolation. Both the perceived position of the bimodal stimuli and the improved precision were well predicted by assuming statistically optimal Bayesian-like combination of visual and auditory signals. Furthermore, the time course of localization was well predicted by the Bayesian approach. We present a detailed model that simulates the time-course data, assuming that perceived position is given by the sum of retinal position and a sluggish noisy eye-position signal, obtained by integrating optimally the output of two populations of neural activity: one centered at the current point of gaze, the other centered at the future point of gaze.