High optical quality nonlinear crystals of solid solution GaSe(1-x)S(x), x=0, 0.05, 0.11, 0.22, 0.29, 0.44, 1 were grown by modified Bridgman method with heat field rotation. Ordinary and extraordinary wave dispersion was studied in detail as a function of sulfur content by terahertz time-domain spectroscopy (THz TDS) in the 0.3-4 THz range using cleaved and processed (cut and polished) crystals. Suitable dispersion equations for different parts of the entire transparency range were derived, utilizing comparative analyses of the measured data, the available published data, and approximations in the form of Sellmeier equations. A criterion was proposed for selecting measurement results of adequate quality, based on the etalon patterns in the transmission spectrum.