We report two fundamental modifications to the Tool-Narayanaswamy-Moynihan (TNM) model on enthalpy relaxation in glasses. Firstly, a generalized stretching function is introduced for the distribution of relaxation times. Secondly, the substantial broadening of the glass transition region due to the hyperquenching process is included. Using the modified model, we have succeeded in accurately modeling the enthalpy response of glasses far from equilibrium to both dynamic heating and static annealing. (C) 2010 Elsevier B.V. All rights reserved.