The representation of the visual world on the retina is constantly changing because of our eye movements, but we perceive the visual world as stable and continuous. To maintain the perceptual stability across saccades, we have to integrate the visual information accurately before and after the saccades in line with the spatiotopic coordinates. To examine how the visual system deals with the spatial localization of moving visual stimuli across saccades, we recorded activities of motion sensitive neurons at middle temporal (MT) and medial superior temporal (MST) areas in awake monkeys. We carried out continuous observation of their receptive fields (RFs) while the monkeys performed fixation and saccade tasks in which a spatially stable moving stimulus was presented at various locations in the visual field. When the moving stimulus was presented for 600 ms throughout the periods before, during, and after the saccades, we found that the location of the RFs moved with the eye position shifts due to the saccades, indicating that the neurons in both areas have retinotopic RFs across the saccades. When the moving stimulus was presented for 170 ms and turned off before the saccades, different characteristics were observed. For MT neurons, no response was observed after the saccade, suggesting that their responses simply reflect reafferent visual information. In contrast, most MST neurons increased their firing rates when a saccade brought the location of the visual stimulus into their RFs, where the visual stimulus no longer existed. The result suggests that the responses of such MST neurons after the saccades were evoked by a memory of the stimulus that had pre-existed in the post-saccadic RFs ("memory remapping"). It indicates that visual information before the saccade is retained and localized in spatiotopic coordinates at other visual area(s) and that extraretinal signals coding the saccade-vector trigger the recall of its representation as neuronal activity in MST. The recalled information that had pre-existed and the renewed information after the saccade are most likely integrated, thus allowing perception of the stable and continuous visual world.