Changes in the enthalpy and entropy on structural relaxation of Mg(65)Cu(2)sTb(10) glass have been studied after keeping its samples for varying periods of time t(d) at several temperatures TdS, and after keeping for fixed t(d) at various TdS. At a fixed T-d, the decrease in the enthalpy and entropy occurred with time according to a non-exponential kinetics. When the sample was kept for the same t(d), but at different TdS the decrease in the enthalpy and entropy showed a peak at a temperature when the sample reached an equilibrium state for that t(d). The fictive temperature estimated from the entropy change was the same as that estimated from the enthalpy change, thus suggesting that irreversibility of the thermodynamic path in the glass-transition range does not have a significant effect on determining the entropy. The rate of heat release from the DSC heating scan was analyzed in terms of the model for non-exponential, non-linear enthalpy relaxation. A single set of parameters that fitted the data for un-annealed glass did not fit the data for the highly annealed glass. This is expected in view of the approximations made in the model and the contribution from the JG relaxation. It is suggested that a model-independent method for studying enthalpy relaxation would be more appropriate. A glass stored at ambient conditions showed an endothermic peak that is attributed partly to the unfreezing of the JG relaxation and partly to those of the faster modes in the distribution of the a-relaxation times. (C) 2010 Elsevier B.V. All rights reserved.