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We experimentally investigated how nanostructuring affects the third-order elastic constants Cijklqr (TOECs) and ultrasonic nonlinear parameter N (NP) of the aluminum alloy AMg6 (Al–Mg–Mn system), and we had prepared a nanocomposite 0.3wt.%C60/AMg6 (n-AMg6) from it. The study of the nonlinear elastic properties was conducted in two ways: TOECs were measured by Thurston-Brugger method and the NPs were measured by spectral method. We also wanted to evaluate how these two methods are consistent and complement each other.