The paper discusses an adaptive strategy to effectively control nonlinear manipulation motions of a dual arm robot (DAR) under system uncertainties including parameter variations, actuator nonlinearities and external disturbances. It is proposed that the control scheme is first derived from the dynamic surface control (DSC) method, which allows the robot's end-effectors to robustly track the desired trajectories. Moreover, since exactly determining the DAR system's dynamics is impractical due to the system uncertainties, the uncertain system parameters are then proposed to be adaptively estimated by the use of the radial basis function network (RBFN). The adaptation mechanism is derived from the Lyapunov theory, which theoretically guarantees stability of the closed-loop control system. The effectiveness of the proposed RBFN-DSC approach is demonstrated by implementing the algorithm in a synthetic environment with realistic parameters, where the obtained results are highly promising