The glass transition dynamics of stacked thin films of polystyrene and poly(2-chlorostyrene) were investigated using differential scanning calorimetry and dielectric relaxation spectroscopy. The glass transition temperature T(g) of as-stacked thin polystyrene films has a strong depression from that of the bulk samples. However, after annealing at high temperatures above T(g), the stacked thin films exhibit glass transition at a temperature almost equal to the T(g) of the bulk system. The α-process dynamics of stacked thin films of poly(2-chlorostyrene) show a time evolution from single-thin-film-like dynamics to bulk-like dynamics during the isothermal annealing process. The relaxation rate of the α process becomes smaller with increase in the annealing time. The time scale for the evolution of the α dynamics during the annealing process is very long compared with that for the reptation dynamics. At the same time, the temperature dependence of the relaxation time for the α process changes from Arrhenius-like to Vogel-Fulcher-Tammann dependence with increase of the annealing time. The fragility index increases and the distribution of the α-relaxation times becomes smaller with increase in the annealing time for isothermal annealing. The observed change in the α process is discussed with respect to the interfacial interaction between the thin layers of stacked thin polymer films.