The problem of modeling and controlling the impact between the end-effecters of two multi-DOF cooperating manipulators is considered in this paper, with the goal of designing a control scheme that brings the end-effecters in a steady-state contact with each other and regulates the robots to desired configurations, with an assigned contact force. The equations of motion of the robots are determined both in the contact condition and in the noncontact one. One controller is designed for each manipulator, independently of the other one, including a reduced-order observer for the estimation of the impact-induced forces; in particular, each controller requires only the position and velocity measurements of the robot on which it is implemented (no force measurement is necessary). Such a control scheme, which works correctly also when the robots do not interact (no switching condition is present), allows the global asymptotic regulation of the cooperating robot arms to the desired configuration, with the prescribed contact force, as it is analytically proven in the paper.