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In this paper, boundary control for a coupled nonlinear flexible marine riser with two actuators in transverse and longitudinal directions is developed to reduce the riser's vibrations. The dynamic behavior of the flexible riser is represented by a distributed parameter system with partial differential equations (PDEs) and the control is applied at the top boundary of the riser based on Lyapunov's direct method to regulate the riser's vibrations. With the proposed boundary control, uniform boundedness under ocean current disturbance, and exponential stability under free vibration condition can be achieved. The proposed control is independent of system parameters, which ensures the robustness of the system to variations in parameters. Numerical simulations for demonstrating the effectiveness of the proposed control are presented.