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This article presents a nonlinear adaptive line-of-sight path following controller for underactuated autonomous underwater vehicles in the presence of ocean currents. Firstly, a new nonsingular path following error kinematic model in the Serret–Frenet frame is developed, where a nominal course angle error is introduced to significantly simplify the guidance law design. Secondly, an adaptive line-of-sight guidance law with the introduction of the current observer is proposed to make the vehicle produce a variable sideslip angle to compensate for the drift force for any parametric curved-path path following. Benefit from the global κ -exponential convergence property of the designed current observer, the actual course angle error can be eliminated indirectly. Then, dynamic controller built on Lyapunov theory and backstepping technique guarantee the uniform global exponential stability of the yaw and relative surge velocity. In the end, stability analysis shows that the global κ -exponential stability is achieved for the closed-loop system. Simulation results demonstrate the effectiveness of the proposed control scheme.