The thermal conductivity, the thermal diffusivity and the heat capacity of AgI-AgPO3 grasses were simultaneously determined during the annealing process of the materials below the glass transition temperature T-g by using an improved hot-wire method developed by the authors. The three thermal quantities showed relaxational behaviors during the annealing, and the relaxation times were determined from the annealing measurement. For example, in (AgI)(0.3)(AgPO3)(0.7); T-g = 108 degrees C, the relaxation times were around 1000-30 min at annealing temperatures of 50-98 degrees C. The observed behavior was considered to be due to a structural relaxation in the glass.