A social Simon effect exists when two individuals perform a Go/No-Go task in the presence of each other, but not when they perform the same task alone. Such effects are argued to indicate that individuals co-represent task goals and the to-be-performed actions of a co-actor. The present study investigates an alternative hypothesis—that these effects are due to dynamical entrainment processes that couple the behavior of socially situated actors. Participants performed a standard Go/No-Go Simon task in joint and individual conditions. The dynamic structure of response times (RTs) was examined using nonlinear methods. Consistent with our hypothesis, the analyses revealed that the structure of RTs in the joint condition indicate interpersonal coupling constraining participant behavior and were more correlated across a range of time-scales compared to the RTs of pseudo-pair controls. The findings imply that dynamic processes might underlie social stimulus-response compatibility effects and shape joint cognitive processes in general.