This paper proposes a method of planning collision-free trajectories for two manipulators considering dynamic constraints. This algorithm is composed of two planning stages. In the first stage, minimum time trajectories for two manipulators are searched with limits of input torques/forces. In the second stage, if there is interference between two obtained trajectories, motion priority is given to two manipulators in order to avoid collision. Collision-free trajectories are obtained along the paths generated in the first stage and their traveling times are shortened, too.