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A combined multiple model adaptive control (CMMAC) scheme, which is a proper combination of the estimator-based MMAC scheme and the unfalsified MMAC scheme, has been proposed with the aim of taking advantage of the strength of each scheme while avoiding their weaknesses. The major novelty of the CMMAC scheme lies in the fact that it monitors not only the adequacy of candidate models in terms of their estimation performances but also the performance of the active candidate controller. As an application of the CMMAC scheme and one example of such new multiple model adaptive controllers, a CMMAC based controller has been designed for a class of nonlinear systems with nonlinear parameterization. Under some sufficient conditions, a strong finite time switching result (which provides a characterization on the maximum number of switching) and the closed-loop stability have been established. A constructive design based on back-stepping is provided for the adaptive control problem of a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability.