Adaptation to motion produces a motion aftereffect (MAE), where illusory, oppositely-directed motion is perceived when viewing a stationary image. A common hypothesis for motion adaptation is that it reflects an imbalance of activity caused by neuronal fatigue. However, the perceptual MAE exhibits storage, in that the MAE appears even after a prolonged period of darkness is interposed between the adapting stimulus and the test, suggesting that fatigue cannot explain the perceptual MAE. We asked whether neural fatigue was a viable explanation for the oculomotor MAE (OMAE) by testing if the OMAE exhibits storage. Human observers were adapted with moving, random-dot cinematograms. Following adaptation, they generated an oculomotor MAE (OMAE), with both pursuit and saccadic components. The OMAE occurred in the presence of a visual test stimulus, but not in the dark. When the test stimulus was introduced after the dark period, the OMAE reappeared, analogous to perceptual MAE storage. The results suggest that fatigue cannot explain the OMAE, and that visual stimulation is necessary to elicit it. We propose a model in which adaptation recalibrates the motion-processing network by adjusting the weights of the inputs to neurons in the middle-temporal (MT) area.