The existence in CdS_1-xSe_x crystals (with x=0.10-0.50) of crystalline regions with stacking faults (SF) was first demonstrated by x-ray diffraction and optical methods. X-ray diffraction studies showed SF to be present in all the samples investigated, but in different concentrations. The effect of SF present in CdS_1-xSe_x solid solutions of different compositions on their exciton reflectance and photoluminescence (PL) spectra has been studied. Crystals with high SF concentrations were found to exhibit new exciton bands, which are manifested in reflectance and PL spectra. In the CdS_1-xSe_x phase with SF, resonant emission due to free excitons and the corresponding phonon replicas have been observed. The effect of reabsorption, which can bring about a change in the zero-phonon emission line shape (doublet formation), as well as affect the intensity ratios of the zero-phonon line to the phonon replicas, has been analyzed. It is pointed out that the variation with temperature of the shape of the SF-induced PL exciton line indicates its complex structure, with the constituents of this structure varying in intensity with increasing temperature.