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This paper proposes a global tracking control method for underactuated ships with input and velocity constraints using the dynamic surface control (DSC) method, where the control structure is formed in a modular way that cascaded kinematic and dynamic linearizations can be achieved similarly as in the backstepping method. First, the first step linearization of the kinematics determines the pseudo (or auxiliary) surge velocity and yaw angle, which are used as the commands for the second-step linearization. Then, in the second-step linearization of dynamics, the actual torque inputs are designed to make the actual surge velocity and yaw angle follow these pseudo commands to achieve the position and yaw angle tracking. By employing the dynamic surface control method in the design of each kinematic and dynamic linearization law, we can obtain a control structure that is much simpler than the previous backstepping-based controllers such that it is beneficial from the practical application viewpoint. In addition, it is possible to track general reference trajectories, i.e., the reference yaw velocity need not be persistently exciting and there is no restriction on the initial yaw tracking error. In particular, global tracking control is achieved even in the presence of input and velocity constraints, unlike the DSC method which introduces the several filters in the backstepping design procedure to avoid the model differentiation and make it easier to be implemented and usually has semiglobal tracking performance. Finally, the stability analysis and numerical simulations are performed to confirm the effectiveness of the proposed scheme.