Adaptive output feedback is applied to an uncertain model of an underactuated underwater vehicle. The vehicle is modelled as a neutrally buoyant, prolate spheroid moving in the longitudinal plane. The two inputs are thrust along the symmetry axis and pitch moment. A linear reference model, which has the same vector relative degree of the system, is designed by linearizing the vehicle dynamics about a trim condition. A linear dynamic compensator is developed for the reference model, causing it to track a given bounded reference command. The input is augmented with an adaptive element and this adaptive control law is applied to the nonlinear system. The adaptive control law is realized using a linearly parameterized neural network which operates over a finite sample of the input-output history.