A new method is presented for the optimal coordination of a two-robot system performing contact operations. One of the robots carries a tool and performs the specific contact operation on a workpiece which is grasped and maneuvered by the second robot. The two robots move simultaneously relative to each other so that the tool maintains contact with the workpiece while moving along its prescribed trajectory at a constant speed. This prescribed trajectory, which is specified with respect to the workpiece frame, is thus resolved into a pair of conjugate trajectories, one for each robot, and specified in the world coordinate frame. This resolution process does not yield a unique solution, i.e. there exist an infinity of conjugate-trajectory pairs corresponding to a given tool trajectory. This paper presents a technique for resolving the original tool trajectory, where the robots’ conjugate trajectories are parameterized using polynomial functions. A method is then developed for selecting the optimal pair of conjugate trajectories on the basis of minimizing a given choice of cost function. This optimization is further enhanced by coupling it to a procedure for selecting the optimal layout of the robots within the workcell, resulting in the best possible solutions. Numerical simulation results support the validity of the proposed technique.