Motion perception relies on at least two distinct systems: a velocity-based motion system (VMS) driven by early direction-selective cells and a position-based system (PMS) tracking objects/features over time and space. However, it remains unclear how these systems interact when they work in parallel. We investigated their roles in the organization of motion information by manipulating a bistable stimulus with eight moving dots that are perceived either as rotating in tandem with their most proximate pair (local motion) or moving around the fixation cross as the corners of two illusory squares (global motion). First, we disrupted VMS by stroboscopically varying interstimulus intervals (ISIs) from 0 to 116.6 ms. This manipulation deactivates the involvement of direction-selective cells, which are known to have short temporal integration windows (<100 ms), undermining VMS. Second, we enhanced different grouping configurations (local-group, global-group, no-group) through contrast polarity. Our findings show that the pattern of bistability changes significantly at ISIs of 33 ms. For ISIs ≥33 ms, static grouping cues strongly influence perceptual bistability. For ISIs <33 ms, the global motion dominates, even with enhanced local grouping cues, suggesting that VMS counteracts static cues. These results highlight distinct rules governing the organization of moving stimuli in VMS and PMS.