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A globally exponentially convergent adaptive observer is proposed for a class of uniformly observable nonlinear systems in order to jointly estimate missing states and unknown constant parameters. The gain of this observer involves a design function that has to satisfy some mild conditions which are given. Different expressions of such a function are proposed. Of particular interest, it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function. Simulation results are presented in order to illustrate the performance of the proposed observer.