The relaxational processes in amorphous solid gentiobiose and cellobiose are studied by thermally stimulated depolarization currents (TSDC) in the temperature region from 108K up to 423K. The slow molecular mobility was characterized in the crystal and in the glassy state. The features of different motional components of the secondary relaxation have been monitored as a function of time as the glass structurally relaxes on aging. It is concluded that some modes of motion of this mobility are aging independent, while others are affected by aging. The value of the steepness index or fragility (T(g)-normalized temperature dependence of the relaxation time) was obtained by differential scanning calorimetry (DSC) from the analysis of the scanning rate dependency of T(g).