We report nonlinear behavior in the motion of driven nanowire cantilevers. The nonlinearity can be described by the Duffing equation and is used to demonstrate mechanical mixing of two distinct excitation frequencies. Furthermore, we demonstrate that the nonlinearity can be used to amplify a signal at a frequency close to the mechanical resonance of the nanowire oscillator. Up to 26 dB of amplitude gain is demonstrated in this way. (C) 2014 AIP Publishing LLC.