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A recursive dynamic modeling and control is presented for the dual-arm manipulator with elastic joints carrying a common object. For decoupling the effect of elastic joints, the dynamic modeling approach is based on the classic recursive Newton-Euler method but involves high-order derivatives of motion and force variables. The high-order inverse kinematics which is needed in the motion control is presented firstly. With the classic Recursive Newton-Euler (RNEA) method, two-order dynamic model of the dual-arm robot is established, for decoupling the effect of the elastic joints, the form of four-order dynamic model is presented, meanwhile, combining with the high-order dynamic model of the carried object, the completed Dual-Arm Elastic Joints Newton-Euler Algorithm (DA-EJNEA) is established. Then the feedback linearization method is adopted to the motion control based on the DA-EJNEA. Finally, to verify the effectiveness of the proposed method, feedback linearization method based on the DA-EJNEA and the computed torque method based on the dynamic model with rigid joints are used to control the dual-arm coordinated system respectively, the simulation results illustrate the feedback linearization method based on the DA-EJNEA has an obvious advantage for trajectory tracking of the object in the operation space, it behaves reasonable potentials for the model-based control.