Values of glass transition temperature (Tg) and of linear expansion coefficient (α) for Asx S100−x glasses were measured in the range of concentrations 35 × 42. Because of the importance of the glass formation region 35 × 42 for the optical fibers elaboration, special attention was made on high-pure Asx S100−x glasses. For the glass in the range of 35 × 38, we measure Tg with the interval of x equal to 1 at.% of arsenic. We also measured the Tg values with the interval of x equal to 0.5 at.% of As. We obtained nonlinear behavior of Tg, reflecting the change in molecular composition of As-S glass in the glass composition range studied. The control of such parameters is important to produce optical fibers with specific numerical aperture.