This paper addresses the problem of dynamic positioning of an underactuated autonomous underwater vehicle (AUV) in the horizontal plane. A nonlinear adaptive controller is proposed that yields convergence of the trajectories of the closed loop system to a desired target point in the presence of a constant unknown ocean current disturbance and parametric model uncertainty. The controller is first derived at the kinematic level assuming that the ocean current disturbance is known. An exponential observer is then designed and convergence of the resulting closed loop system is analyzed. Finally, integrator backstepping and Lyapunov based techniques are used to extend the kinematic controller to the dynamic case and deal with model parameters uncertainties. Simulation results are presented and discussed.