Most animal species group together and coordinate their behavior in quite sophisticated manners for mating, hunting, or defense purposes. In humans, coordination at a level (the pacing of movements) is evident both in daily life (e.g., walking) and skilled (e.g., music and dance) behaviors. By examining the fine structure of movement, we here show that interpersonal coordination is established also at a - movement - level. Natural movements appear as marked by recurrent (2-3 Hz) speed breaks, i.e., submovements, that are traditionally considered the result of intermittency in (visuo)motor feedback-based control. In a series of interpersonal coordination tasks, we show that submovements produced by interacting partners are not independent but alternate tightly over time, reflecting online mutual adaptation. These findings unveil a potential core mechanism for behavioral coordination that is based on between-persons synchronization of the intrinsic dynamics of action-perception cycles.