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In this brief, we consider the problem of adaptive backstepping control of the Chua's circuits with all the parameters unknown. First, we show that several types of Chua's circuits, including the Chua's oscillator, Chua's circuit with cubic nonlinearity, and Murali-Lakshmanan-Chua circuit, can be transformed into a class of nonlinear systems in the nonautonomous "strict-feedback" form. Second, an adaptive backstepping with tuning functions method is extended to this nonautonomous "strict-feedback" system, and then employed to control the output of the Chua's circuit to asymptotically track an arbitrarily given reference signal generated from a known, bounded and smooth nonlinear reference model. Both global stability and asymptotic tracking of the closed-loop system are guaranteed. Simulation results are presented to show the effectiveness of the approach.