The stabilization problems of an underactuated symmetric surface vessel and underactuated non-symmetric surface vessel are considered.Firstly,there exists a natural change of coordinates that transforms the whole dynamical system into a cascade nonlinear system.Secondly,the control problem of the resulting system can be reduced to the stabilization of a third-order chained form.A time-invariant discontinuous feedback law is derived to guarantee global uniform asymptotic stabilization of the system to the desired configuration.The construction of such a controller is based on the backstepping design approach.Finally,simulation results show the effectiveness of the proposed method.