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The path following control problem of autonomous underwater vehicles is addressed in this paper. In order to deal with the parameter variations and uncertainties due to time-varying hydrodynamic damps, the radial basis function neural network (RBF NN) is introduced to estimate unknown terms where an adaptive law is chosen to guarantee optimal estimation of the weight of NN. Based on the Lyapunov stability theorem, an adaptive NN controller is designed to guarantee all the error states in the path following system are asymptotically stable. In order to deal with the estimation error and current disturbance, a virtual control input is introduced to ensure that the error system, including position error and heading error, can be converged to zero. On other hand, the arc with an appropriate radius is specified for each waypoint to guarantee a high accuracy when the vehicle maintains a nominal constant speed. Two path profiles, one with straight lines, and the other with straight-line and arcs were used to evaluate the performance of the path following controller. Simulation results demonstrated that the proposed controller was effective to eliminate the disturbances caused by vehicle's nonlinear and model uncertainty.