A new type of control law is developed to steer an autonomous underwater vehicle (AUV) along a desired path. The methodology adopted for path-following deals explicitly with vehicle dynamics. Furthermore, it overcomes stringent initial condition constraints that are present in a number of path-following control strategies described in the literature. Controller design builds on Lyapunov theory and backstepping techniques. The resulting nonlinear feedback control law yields convergence of the path-following error trajectory to zero. Simulation results illustrate the performance of the control system proposed.