The aim of the present study is to elucidate the influence of context on the kinematics of the reach-to-grasp movement. In particular, we consider two basic modes of social cognition, namely cooperation and competition. In two experiments kinematics of the very same action--reaching-to-grasp a wooden block--were analyzed in two different contexts provided by a cooperative task and competitive task. For the "cooperation" tasks two participants were required to reach and grasp their respective objects and to cooperate to join the two objects in specific configurations in the middle of the working surface. For the "competition" tasks, the two participants had to compete to place their own object first in the middle of the working surface. Results revealed specific kinematic patterns for cooperation and competition which were distinct from similar actions performed by each participant in isolation. Further, during the cooperation tasks, a high level of correlation between key kinematical parameters of the two participants was found. In accordance with evidence from neuroimaging, developmental and social psychology our results suggest the existence of motor patterns which reflect the intention to act in a social context.