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This paper presents a robust actuator fault reconstruction scheme for linear uncertain systems using sliding mode observers. In existing work, fault reconstruction via sliding modes is limited to either linear certain systems subject to unknown inputs, relative degree one systems or a specific class of relative degree two systems. This paper presents a new method that is applicable to a wider class of systems with relative degree higher than one, and can also be used for systems with more unknown inputs than outputs. The method uses two sliding mode observers in cascade. Signals from the first observer are processed and used to drive the second observer. Overall this results in actuator fault reconstruction being feasible for a wider class of systems than existing methods. In this paper the results are applied to an aircraft system.