We have prepared GexGa4S96-x glasses for x=22.5, 27, 30 and 33.3 and GexGa8S92-x for x=32, 36 and measured their linear and nonlinear optical properties. The glasses exhibit broad transmission at a wavelength range from 1 to 12 μm. The evolution of linear, nonlinear index and two-photon absorption as a function of the content of Ge, and the relationship of n2 and β with linear refractive index and optical bandgap are analyzed. While the evolution of n2 and β is closer to the prediction by Sheik-Bahae et.al for optical nonlinearity of semiconductors. Eg of Ge-Ga-S is found to vary from 2.33 to 2.99eV, and the largest nonlinear index is 1.16×10-14cm2/W at composition of Ge32Ga8S60 .