Enthalpy relaxation of hyperquenched phosphate & silicate glasses during annealing is studied using a differential scanning calorimeter (DSC). Results show that proper annealing below the glass transition temperature leads to a calorimetric pre-endotherm followed by an exotherm below the Tg endotherm. The pre-endotherm & exotherm are distinguished by a crossover temperature. With an increase in annealing temperature & time, the endotherm becomes more pronounced, whereas the exotherm gradually disappears. Hyperquenching & annealing are a requisite for the appearance of the pre-endotherm. The extent of the pre-endotherm depends on annealing conditions. The pre-endotherm shows recovery behaviour under certain annealing & DSC-scanning conditions. The origin of the pre-endotherm is fundamentally different from that of the glass transition endotherm.