<p>Perception of a continuous world relies on our ability to integrate discontinuous sensory signals when we make saccadic eye movements, which abruptly change the retinal image. Here we investigate the role of oscillations in integrating pre-saccadic information with the current sensory signals. We presented to participants (<i>N</i> = 24) a brief pre-saccadic Gabor stimulus (termed the <i>inducer</i>) before voluntary 16° saccades, followed by a <i>test</i> Gabor stimulus at various times before or after saccadic onset. Orientation judgments of the test stimulus were biased towards the orientation of both the inducer and previous (1-back) test stimulus, consistent with serial dependence. In addition to the average bias, judgments oscillated in synchrony with saccadic onset at alpha frequencies (~9.5 Hz) towards the orientation of the inducer or 1-back stimulus. There was also a strong bias towards the mean orientation (central tendency): however, that bias was constant over time, not associated with saccade-synched oscillations. Perceptual oscillations in serial dependence (but not central tendency) suggest that alpha rhythms may be instrumental in communicating short-term (but not long-term) perceptual memory across saccades, helping to preserve stability during saccades. The distinction between the modes of communicating short- and long-term memory suggests that the two phenomena are mediated by distinct neuronal circuitry.</p>