Visual perception seems continuous, but recent evidence suggests that the underlying perceptual mechanisms are in fact periodic—particularly visual attention. Because visual attention is closely linked to the preparation of saccadic eye movements, the question arises how periodic attentional processes interact with the preparation and execution of voluntary saccades. In two experiments, human observers made voluntary saccades between two placeholders, monitoring each one for the presentation of a threshold-level target. Detection performance was evaluated as a function of latency with respect to saccade landing. The time course of detection performance revealed oscillations at around 4 Hz both before the saccade at the saccade origin and after the saccade at the saccade destination. Furthermore, oscillations before and after the saccade were in phase, meaning that the saccade did not disrupt or reset the ongoing attentional rhythm. Instead, it seems that voluntary saccades are executed as part of an ongoing attentional rhythm, with the eyes in flight during the troughs of the attentional wave. This finding for the first time demonstrates that periodic attentional mechanisms affect not only perception but also overt motor behavior.