In this work we present a model to explain the compositional dependence of the optical (Tauc) gap for a-Si, S:H and a-Si, Se:H alloys. Thin films of these materials were grown by a capacitively coupled r.f. glow-discharge decomposition of silane and either hydrogen sulfide or hydrogen selenide gases. The compositional dependence was obtained by varying the gas volume ratio R v = H 2 S or H 2 S e / S i H 4 . Optical transmission measurements were employed to measure the optical (Tauc) gap of both alloys as a function of the gas volume ratio. The compositional dependence exhibits an inverted S-shaped variation. A model was developed that fits accurately the experimental data. It was shown that the parameters of the fitting curve are directly and accurately related to some fundamental atomic constant.