In this work we formulate a new glass theory and investigate its suitability for describing the mechanical response of thermoplastic elastomers composed of styrenic-block copolymers. These materials are composed of glassy domains of polystyrene, which physically link soft rubbery chain segments made of either polybutadiene or polyisoprene. We demonstrate that the crossover in the shift factors, observed experimentally to change from Williams-Landel-Ferry to Arrhenius behavior passing through a characteristic crossover temperature T* from below, coincides with the crossover from power-law to stretched-exponential behavior of the stress relaxation found in recent tensile experiments. Moreover, we show that the characteristic crossover temperature T* is identical with the underlying true equilibrium second-order phase transition temperature T-2 of the polystyrene crosslinks, predicted by the thermodynamic theory of Gibbs and Di Marzio for pure glassy polystyrene in the infinite-time limit. By combining the recently introduced theory of Di Marzio and Yang with the significant-structure theory of Eyring and Ree, we develop a new glass theory, which is capable of explaining the mechanical response of multiphase as well as pure glassy materials. Moreover, we show a clear evidence for the existence of T-2 postulated in 1950s for pure glasses and hotly debated since then. (c) 2006 Elsevier Ltd. All rights reserved.