Nondegenerate four-wave mixing technique has been used to investigate the third-order nonlinear susceptibility for nanocomposite material with Au nanocrystals formed inside a SiO2 glass matrix. High concentrations of encapsulated Au nanocrystals are formed by implantation of Au+ ions into fused silica glass substrates and thermal annealing. The size distribution and the depth profiles of the Au nanoparticles can be controlled by the implantation dose, energy and annealing temperatures. The high value of the third-order susceptibility approximately (0.26 - 1.3) X 10-7 esu was found in the range of the frequency detunings (Delta) (1/(lambda) ) -1 near the surface plasmon resonance. Two characteristic relaxation times, 0.66 ps and 5.3 ps, have been extracted from the detuning curve of the third-order susceptibility as the probe-beam frequency changes and the pump-beam frequency fixed at the plasmon resonance. The first relaxation time was attributed to electron-phonon relaxation, and the second to thermal diffusion to the host medium. The efficient nondegenerate conversion is attractive for optical processing.