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Due to the aperture problem, the initial direction of tracking responses to a translating bar is biased towards the direction orthogonal to the bar. This observation offers a powerful way to explore the interactions between retinal and extraretinal signals in controlling our actions. We conducted two experiments to probe these interactions by briefly (200 and 400 ms) blanking the moving target (45° or 135° tilted bar) during steady state (Experiment 1) and at different moments during the early phase of pursuit (Experiment 2). In Experiment 1, we found a marginal but statistically significant directional bias on target reappearance for all subjects in at least one blank condition (200 or 400 ms). In Experiment 2, no systematic significant directional bias was observed at target reappearance after a blank. These results suggest that the weighting of retinal and extraretinal signals is dynamically modulated during the different phases of pursuit. Based on our previous theoretical work on motion integration, we propose a new closed-loop two-stage recurrent Bayesian model where retinal and extraretinal signals are dynamically weighted based on their respective reliabilities and combined to compute the visuomotor drive. With a single free parameter, the model reproduces many aspects of smooth pursuit observed across subjects during and immediately after target blanking. It provides a new theoretical framework to understand how different signals are dynamically combined based on their relative reliability to adaptively control our actions. Overall, the model and behavioral results suggest that human subjects rely more strongly on prediction during the early phase than in the steady state phase of pursuit.