Nanoscale phase separation effects are of general interest in glass science. Such structural effects produce usually pronounced changes in glass physical properties which can mask the more subtle elastic effects related to rigidity transitions. The glass-transition temperature, Tg, is an intrinsic measure of network connectivity. It can be expected to increase or decrease as a network polymerizes or nanoscale phase separates. Compositional trends in Tg(x) in binary AsxSe1–x and GeySe1–y glasses show thresholds near the stoichiometric compositions, x = 2/5 or a mean coordination number r =2.4 , y = 1/3 or r =2.67 . These Tg trends in conjunction with spectroscopic (Raman, Mossbauer) evidence of broken chemical order suggest that the stoichiometric glasses As2Se3 and GeSe2 consist of a Se-rich majority phase that is separate from a compensating Ge- or As-rich minority phase, i.e., they are nanoscale phase separated. On the other hand, ternary Gex(As or P)xSe1–2x glasses containing equal proportions of the group IV and V elements reveal compositional trends in Tg(x) that increase monotonically with x; they appear to polymerize increasingly over a wide 2 r =2.40 . Previous claims of a rigidity transition near r =2.67 can be traced to nanoscale phase separation effects.