The problem of the existence and structure of minimum-time control for multiple robot arms cooperatively handling a common object is addressed. The dynamical system is modeled by considering the arms as closed kinematic chains. The conditions of the existence of the time-optimal solution are verified by applying a Lyapunov approach and the concept of the feedback equivalence to linear systems. Furthermore, it is shown that the structure of the minimum-time control law for individual joint actuators requires that at least one of the actuators is always saturated on any finite time subinterval, while the rest of them are either saturated or singular, depending upon the motion configurations and robot parameters. Thus, it is suggested that totally-singular optimal control does not exist in this problem, but that partially-singular control may occur. This theoretical result should be able to provide insight into the dynamic characteristics of the multiple robot system, which can be valuable in the path planning and design specifications of the system.