This article deals with the problem of timevarying parameter identification in dynamical regression models affected by disturbances. The disturbances comprise timedependent external perturbations and nonlinear unmodeled dynamics. With this aim in mind, we propose a robust nonlinear adaptive observer. The algorithm ensures the asymptotic convergence of the parameter identification error to an acceptably small region around the origin in the presence of disturbances. The synthesis of the adaptive observer is given in terms of linear matrix inequalities, providing a constructive design method. An academic example and a low inertia power system illustrate the robustness and the applicability of the proposed adaptive observer for the time-varying parameter identification problem.