The problem of tracking a Cartesian space trajectory for an object held by two redundant robots while controlling the contact force and the object's internal force is investigated in this paper. A two-level impedance control (TLIC) algorithm incorporating an error reference controller (ERC) is developed. This algorithm is robust to system and environmental kinematic and dynamic uncertainties. Joint redundancy is used to fulfil additional tasks such as singularity robustness. The control algorithm is applicable to dual independent as well as closed-chain robot control. The algorithm has been extensively tested using a computer simulation of the full dynamic model of a dual-arm experimental redundant system in our Robotics and Control Systems Laboratory. The algorithm has also been implemented on the dual-arm experimental system. Experimental results that illustrate various features of the dual-arm control algorithm are presented in this paper.