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Motivated by constant parameter estimation in nonlinear models, as well as state observation in dynamical systems, an adaptive observer is proposed for a class of nonlinear systems linearly depending on unknown parameters. This observer is derived from the well-known high-gain nonlinear design on the one hand, and an adaptive linear one on the other hand, on the basis of previous results in that direction (Xu, 2002). Global exponential convergence is shown under appropriate excitation conditions, and the results are illustrated by simulations.