Saccadic adaptation maintains the correct mapping between eye movements and their targets, yet the dynamics of saccadic gain changes in the presence of systematically varying disturbances has not been extensively studied. Here we assessed changes in the gain of saccade amplitudes induced by continuous and periodic postsaccadic visual feedback. Observers made saccades following a sequence of target steps either along the horizontal meridian (Two-way adaptation) or with unconstrained saccade directions (Global adaptation). An intrasaccadic step—following a sinusoidal variation as a function of the trial number (with 3 different frequencies tested in separate blocks)—consistently displaced the target along its vector. The oculomotor system responded to the resulting feedback error by modifying saccade amplitudes in a periodic fashion with similar frequency of variation but lagging the disturbance by a few tens of trials. This periodic response was superimposed on a drift toward stronger hypometria with similar asymptotes and decay rates across stimulus conditions. The magnitude of the periodic response decreased with increasing frequency and was smaller and more delayed for Global than Two-way adaptation. These results suggest that—in addition to the well-characterized return-to-baseline response observed in protocols using constant visual feedback—the oculomotor system attempts to minimize the feedback error by integrating its variation across trials. This process resembles a convolution with an internal response function, whose structure would be determined by coefficients of the learning model. Our protocol reveals this fast learning process in single short experimental sessions, qualifying it for the study of sensorimotor learning in health and disease.