The paper is devoted to the online identification of the nonlinear model of surface vessel dynamics. The mathematical formulation of the maritime ships is complicated due to the existence of nonlinear hydrodynamic forces and moments that are associated with vessel dynamics. For this reason, the coefficients of the model are not known, nor do they require clarification. The identification algorithm is based on the method of the dynamic regressor extension and mixing (DREM). On the first step using parameterisation, the regression model is obtained, where regressor and regressand depend on measurable signals: linear velocities in surge, the linear velocity in sway, the angular velocity in yaw and the rudder angle. At the second step, the new regression model is obtained using linear stable filters and delays. DREM allows replacing the regression model of the nth order with n first order regression models and estimate parameters separately. Finally, parameters are estimated by the standard gradient descent method. The efficiency of the proposed approach is demonstrated through a set of numerical simulations.