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This paper treats the design problem of full-order observers for nonlinear descriptor systems with unknown input (UI). Depending on the available knowledge on the UI dynamics, two cases are considered. First, a UI proportional observer (UIPO) is proposed when the spectral domain of the UI is unknown. Second, a PIO is proposed when the spectral domain of the UI is in the low frequency range. Sufficient conditions for the existence and stability of such observers are given and proved. Based on the linear matrix inequality (LMI) approach, an algorithm is presented to compute the observer gain matrix that achieves the asymptotic stability objective. An example is included to illustrate the method.