The isothermal enthalpy relaxation of glycerol and propylene glycol is studied for different subglass transition annealing temperatures using our usual method. The kinetics of the glass transition is analyzed using the Kohlrausch-Williams-Watts model. The Vogel-Fulcher-Tamman model was previously used for the spectrometric specific heat analysis of glycerol and propylene glycol by Birge and co-workers at temperatures higher than the glass transition. We present the comparison of the enthalpy relaxation times as a continuation of their data for sub-glass transition temperatures. The results show an intermediate thermal domain between the liquid state and the glassy state. The relaxation times are experimentally determined within the model of the non-exponential relaxation theory. The effects of the cooling and warming rates are also investigated for their relevance in the determination of the relaxation times.