Previous work has shown that the ability to track with the eye a moving target is substantially improved when the target is self-moved by the subject's hand compared with when being externally moved. Here, we explored a situation in which the mapping between hand movement and target motion was perturbed by simulating an elastic relationship between the hand and target. Our objective was to determine whether the predictive mechanisms driving eye-hand coordination could be updated to accommodate this complex hand-target dynamics. To fully appreciate the behavioral effects of this perturbation, we compared eye tracking performance when self-moving a target with a rigid mapping (simple) and a spring mapping as well as when the subject tracked target trajectories that he/she had previously generated when using the rigid or spring mapping. Concerning the rigid mapping, our results confirmed that smooth pursuit was more accurate when the target was self-moved than externally moved. In contrast, with the spring mapping, eye tracking had initially similar low spatial accuracy (though shorter temporal lag) in the self versus externally moved conditions. However, within ∼5 min of practice, smooth pursuit improved in the self-moved spring condition, up to a level similar to the self-moved rigid condition. Subsequently, when the mapping unexpectedly switched from spring to rigid, the eye initially followed the expected target trajectory and not the real one, thereby suggesting that subjects used an internal representation of the new hand-target dynamics. Overall, these results emphasize the stunning adaptability of smooth pursuit when self-maneuvering objects with complex dynamics.