The objective of the project is to develop and evaluate controller designs based on backstepping technique, for an unmatched asymmetric electro-hydraulic system with highly non-linear characteristics, large disturbances and parameter variations. To reach this objective a non-linear model of the system is developed and verified using experiments. The design and derivation of a robust adaptive backstepping controller with both nonlinear and linear parameter adaption is designed and proven globally uniformly asymptotically stable within a predefined constant tracking bound. A simplified backstepping controller is also proposed. This design is based on the larger and more complex backstepping controller but the inner control loop uses a simplified and linearized model for the pressure dynamics, to reduce the number of parameters and make the design realizable in the experimental setup. The robustness of this controller was shown both using simulations and experimental results, and is showed good tracking performance despite large parameter variations and disturbances in simulations.