Two adaptive failure compensation control schemes based on MRAC are developed for a class of MIMO LTI systems with unknown actuator failures. An effective controller structure is proposed to achieve the desired plant-model output matching when implemented with matching parameters. Design conditions are specified for such nominal plant-model output matching. Two adaptive versions of the nominal controller are proposed and stable adaptive laws are derived for updating the controller parameters when plant parameters and failure parameters are unknown. All closed-loop signals are bounded and the plant outputs track the given reference outputs asymptotically, despite the uncertainties in actuator failures and plant parameters. Simulation results for an aircraft lateral dynamic model verify the desired adaptive control system performance in the presence of unknown rudder and aileron failures.