The complex dynamics that characterize hydraulic systems make it difficult for the control design to achieve prescribed goals in an efficient manner. In this paper, we present the design and analysis of a robust nonlinear controller for a nonlinear hydraulic-mechanical (NHM) system. The system consists of an electrohydraulic servo valve and two hydraulic cylinders. Specifically, by considering a part of the dynamics of the NHM system as a norm-bounded uncertainty, two adaptive controllers are developed based on the backstepping technique that ensure the tracking error signals asymptotically converge to zero despite the uncertainties in the system according to the Barbalat lemma. The resulting controllers are able to take into account the interval uncertainties in Coulomb friction parameters and in the internal leakage parameters in the cylinders. Two adaptation laws are obtained by using the Lyapunov functional method and inequality techniques. Simulation results demonstrate the performance and feasibility of the proposed method.