Research results for the nonlinear elastic characteristics of the polycrystalline aluminum alloy AMg6 and AMg6/C60 nanocomposite (n-AMg6) have been described. The ultrasonic study of the elastic characteristics at pressures up to 1.6 GPa has been carried out using a high-pressure ultrasonic piezometer based on the piston-cylinder device. Pressure dependencies of the longitudinal and shear elastic waves velocities and densities of AMg6 and n-AMg6 were experimentally measured and the pressure derivatives of the secondorder elastic constants were calculated. The results derived by this method have been compared with the results of studies of the nonlinear elastic properties of the test alloys using the Thurston–Brugger quasi-static method, where third-order elastic constants have been measured. The relationships between the pressure derivatives of the second-order elastic constants of these alloys and the Mg-content and nanostructuring were established.