The annealing effects are studied based on the comparison between the experimental results and the calculated ones by the phenomenological model equation with parameters obtained by the quasi-isothermal temperature modulated differential scanning calorimetry. We have clarified that the shift of the maximum temperature in specific heat toward low and high temperatures with annealing time originates from the two effects produced by the annealing; the decay of enthalpy toward the equilibrium and an increase in the relaxation time during annealing. We have also clarified the origin of two maxima in specific heat observed at high and low temperatures in the glass transition region in the annealing experiments in polymethyl methacrylate(PMMA). The higher maximum originates from the history of cooling and heating, and the lower one, from the annealing history. We have proposed that the apparently different behavior in enthalpy relaxation in polystyrene and PMMA is originated from the same mechanism.