This paper proposes a trajectory generation method for multiple manipulators through cooperative and competitive interactions among subsystems corresponding to each manipulator. The method can generate the trajectories of multiple manipulators in a parallel and distributed way using virtual dynamics. The virtual dynamics for each manipulator result in virtual interaction forces which represent the interaction among manipulators. It is shown that the method is effective not only for simple cooperative tasks such as positioning a common object, but also for more complicated tasks including relative motions among manipulators.