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A resilient and robust finite-time bounded observer design is derived for a class of nonlinear systems with nonlinear measurement equations, both having vanishing nonlinear model perturbations and additive disturbances. The observer is robust for all vanishing nonlinear perturbations in the system model and measurements, and it is resilient against bounded perturbations in the observer gain. Therefore, in the presence of unknown and vanishing nonlinear perturbations and additive disturbances with known waveforms, the estimation error magnitude remains below a prescribed bound over a finite-time interval. Furthermore, under special conditions, the estimation error can also be made asymptotically stable. A Luenberger type nonlinear observer is used to find an estimate of the unknown state vector from the available measurements. A set of conditions, representing a set of linear matrix inequalities, which guarantee the existence of such an observer and allow a solution for the observer gain and the bound on the maximum allowable gain perturbation is derived. The paper is concluded with a numerical example, which illustrates the applicability of the observer design.