In our problem of fixtureless assembly, two robot manipulators are required to force two elastically deformable sheet metal parts together for welding by a third robot while following a desired trajectory. This thesis focuses on the control problem in which the positions of the pans and the contact forces between them must be regulated. Two position/force control schemes are formulated based on only the rigid dynamics of the system due to unavailable measurement of the flexible states of the payload. The first is an independent control scheme in which one robot is position controlled using a modified version of the computed torque control law while the other is position/force controlled using a discontinuous control law that allows stable switching from non-contact to contact tasks. The second approach is a coordinated control scheme that treats the two robots as a single system. The coordinated control law has the same general form as the independent hybrid control law except in the definition of the task dependent generalized coordinates. The stability of the closed-loop system under the independent rigid hybrid controller is analyzed using the theory associated with singularly perturbed systems. The proposed control schemes are implemented along with the standard PID position controller on two C'HS Robotics Corporation A460 industrial robots in our laboratory. The results show that tfit PID or any other position controllers can not meet the control objectives. Both hybrid schemes are shown to achieve the control objectives with the independent scheme showing superior performances for the particular experimental tasks.