This paper proposes a nonlinear robust adaptive control strategy to force a six degrees of freedom underactuated underwater vehicle with only four actuators to follow a predefined path at a desired speed despite of the presence of environmental disturbances and vehicle's unknown physical parameters. The proposed controller is designed using Lyapunov's direct method, the popular backstepping and parameter projection techniques. The closed-loop path following error can be made arbitrarily small. Numerical simulations are provided to illustrate the effectiveness of the proposed methodology for the path following of underactuated underwater vehicles.