The structure of binary glasses is elucidated using modulated differential scanning calorimetry, Raman scattering, IR reflectance, and molar volume experiments over a wide range of compositions. We observe a reversibility window in the calorimetric experiments, which permits fixing the three elastic phases: flexible at , intermediate in the range, and stressed rigid at . Raman scattering supported by first-principles cluster calculations reveals that the observed vibrational density of states has features of both pyramidal (PYR) and quasitetrahedral (QT) local structures. The QT unit concentrations show a global maximum in the intermediate phase (IP), while the concentration of PYR units becomes comparable to those of QT units in that phase, suggesting that both these local structures contribute to the width of the IP. The IP centroid in the sulfides is shifted to lower As content than in corresponding selenides, a feature identified with excess chalcogen partially segregating from the backbone in the sulfides, but forming part of the backbone in selenides. These ideas are corroborated by the proportionately larger free volumes of sulfides than selenides and the absence of chemical bond-strength scaling of ’s between As sulfides and As selenides. Low-frequency Raman modes increase in scattering strength almost linearly as As content of glasses decreases from to 8% and glasses become flexible, with a slope that is close to the floppy mode fraction predicted by rigidity theory. These results show that floppy modes contribute to the excess vibrations observed at low frequency. In the intermediate and stressed rigid elastic phases low-frequency Raman modes persist and are identified as boson modes. Some consequences of the present findings on the optoelectronic properties of these glasses are commented upon.