This paper develops a robust non-linear controller that asymptotically drives the dynamic model of an AUV onto a predefined path at a constant forward speed. A kinematic controller is first derived, and extended to cope with vehicle dynamics by resorting to backstepping and Lyapunov-based techniques. Robustness to vehicle parameter uncertainty is addressed by incorporating a hybrid parameter adaptation scheme. The resulting nonlinear adaptive control system is formally shown and yields asymptotic convergence of the vehicle to the path. Simulations illustrate the performance of the derived controller.