Periodicity is a fundamental property of biological systems, including human movement systems. Periodic movements support displacements of the body in the environment as well as interactions and communication between individuals. Here, we use electroencephalography (EEG) to investigate the neural tracking of visual periodic motion, and more specifically, the relevance of spatiotemporal information contained at and between their turning points. We compared EEG responses to visual sinusoidal oscillations versus nonlinear Rayleigh oscillations, which are both typical of human movements. These oscillations contain the same spatiotemporal information at their turning points but differ between turning points, with Rayleigh oscillations having an earlier peak velocity, shown to increase an individual's capacity to produce accurately synchronized movements. EEG analyses highlighted the relevance of spatiotemporal information between the turning points by showing that the brain precisely tracks subtle differences in velocity profiles, as indicated by earlier EEG responses for Rayleigh oscillations. The results suggest that the brain is particularly responsive to velocity peaks in visual periodic motion, supporting their role in conveying behaviorally relevant timing information at a neurophysiological level. The results also suggest key functions of neural oscillations in the Alpha and Beta frequency bands, particularly in the right hemisphere. Together, these findings provide insights into the neural mechanisms underpinning the processing of visual periodic motion and the critical role of velocity peaks in enabling proficient visuomotor synchronization.