The motion after-effect (MAE) lasts longer when the test period does not immediately follow adaptation, a phenomenon called storage. Does storage of the MAE occur if the test target is present but rendered phenomenally invisible owing to the presence of a rival target presented to the other eye during the storage period? Our experiment addressed this question. Following adaptation to a drifting grating, an intervening period preceded testing with a stationary grating. During this period, the adapted eye either viewed the test target immediately or was occluded, and the unadapted eye either viewed a high-contrast rival target or was occluded. Thus four conditions were employed. The duration of the residual MAE was found to be longer for the rivalry condition (grating and rival target viewed) than for the normal MAE condition (grating viewed), and comparable to that in the stored MAE condition (both eyes occluded). Thus, the MAE is stored when the test target is rendered invisible due to binocular rivalry, indicating that a suppressed target is ineffective at promoting decay of the MAE. So while suppression does not prevent information about the adapting grating from reaching the site of generation of the MAE (Lehmkuhle & Fox, 1975), it can prevent information about the test target from reaching the site of the stored MAE. Current models attribute the MAE to reduced responsiveness of direction-selective cortical neurons (Sutherland, 1961; Barlow & Hill, 1963). Thus, storage should reflect a differential return of these adapted cells to preadapted response levels, dependent on postadaptation stimulation. From our results we deduce that storage does not occur at all sites at which motion adaptation occurs. Rather, decay of the MAE is dependent on postadaptation stimulation at higher levels of adaptation, and independent at earlier levels.