In two experiments, we examined the extrapolation of a constant-velocity motion along a fixed circular path in the frontal plane. A target moved over an arc of 90 deg and then disappeared. Observers were to assume that the motion continued at the original velocity. After a variable time, a line appeared at another point on the circle to mark the end of the (invisible) 'motion'. Observers decided whether or not the target would have passed this end line, and gave a pass/no-pass response. In Experiment 1, a time course was established for the observed loss in accuracy with increasing duration of invisible motion. Two models of accuracy loss were constructed and tested. Both models assume that (1) extrapolation is performed by 'tracking' the position of the hidden target, and (2) there is no systematic velocity error in tracking, only random variation in tracker velocity. Both models predicted changes in hit and false alarm rates well, except in a condition where response asymmetries were present. In Experiment 2, the hypothesis that observers were tracking the hidden target was assessed by presenting a moving distractor during part of the trial. The presence of the distractor reduced performance under some conditions, suggesting that target tracking was occasionally disrupted. Grossly unequal distributions of pass/no-pass responses were observed for the fastest (8 deg/sec) and slowest (4 deg/sec) target velocities. However, the variable tracker models, using the parameter values from the first experiment, made accurate predictions for the 6 deg/sec condition, in which response distribution was nearly equal. Thus, there may be no need to posit systematic velocity error in motion tracking during extrapolation. The time course of accuracy decline can be accounted for by random variation in tracker velocity when response bias is absent.