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A method for decomposition of a multicomponent nonstationary signal is presented. In this method a nonlinear adaptive structure, which was first introduced as a sinusoidal tracking algorithm, is used. This structure provides excellent (instantaneous) frequency-adaptivity and (instantaneous) amplitude-adaptivity features; These features make it an ideal IF-IA estimator for a monocomponent nonstationary signal. We show that a parallel-scheme of this structure decomposes a multicomponent nonstationary signal into its composite monocomponent nonstationary signals and, moreover, estimates IF and IA of each component accurately. Unlike most other approaches in the literature, which use the complex representation for the given signal, this method employs a real representation for it. High resolution in time-frequency plane, cross terms free, simple structure, and the capability of real-time implementation are among significant features of this method. Results on both simulated and real data, i.e. a bat echolocation signal, are given to confirm the above-mentioned performances.