In cooperative manipulation with multiple robot arms or multifingered robot hand handling a single object, simultaneous control of the object motion and of the internal force exerted by arms or fingers on the object are required. Furthermore, in case where the motion of the object is constrained in some directions due to a contact with its environment, control of the constraint force also becomes necessary. In this paper, for controlling motion of an object under constraint as well as constraint force and internal force, a cooperative dynamic hybrid control method for multiple robotic mechanisms is proposed. This method takes the manipulator dynamics and object dynamics into consideration. An experimental result is presented which shows the validity of the proposed approach.