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In this paper, a class of nonlinear systems with uncertain parameters is considered. A novel adaptive law is designed to identify unknown parameters under the assumption that the time derivative of some of the outputs is measurable. Then, a sliding-mode observer is proposed to estimate the system state variables. By using the inherent features of sliding-mode observers, a fault-reconstruction scheme is proposed which can be implemented online. The proposed reconstruction signal can approximate the fault signal to any required accuracy even in the presence of uncertain parameters. A simulation example for a magnetic-levitation system is given to illustrate the feasibility and effectiveness of the proposed scheme.