The dynamic properties of water confined within nanospaces are of interest given that such water plays important roles in geological and biological systems. The enthalpy-relaxation properties of ordinary and heavy water confined within silica-gel voids of 1.1, 6, 12, and 52 nm in average diameter were examined by adiabatic calorimetry. Most of the water was found to crystallize within the pores above about 2 nm in diameter but to remain in the liquid state down to 80 K within the pores less than about 1.6 nm in diameter. Only one glass transition was observed, at T(g) = 119, 124, and 132 K for ordinary water and T(g) = 125, 130, and 139 K for heavy water, in the 6-, 12-, and 52-nm diameter pores, respectively. On the other hand, two glass transitions were observed at T(g) = 115 and 160 K for ordinary water and T(g) = 118 and 165 K for heavy water in the 1.1-nm pores. Interfacial water molecules on the pore wall, which remain in the noncrystalline state in each case, were interpreted to be responsible for the glass transitions in the region 115-139 K, and internal water molecules, surrounded only by water molecules in the liquid state, are responsible for those at 160 or 165 K in the case of the 1.1-nm pores. It is suggested that the glass transition of bulk supercooled water takes place potentially at 160 K or above due to the development of an energetically more stable hydrogen-bonding network of water molecules at low temperatures.