Water involved in a polyelectrolyte: Membrane of Nafion has recently been revealed to comprise three distinctive molecular species with respect to molecular Motion correlated with the hydrogen bonding structure by using H-1 NMR, infrared, and mass spectrometries. The three species are assigned to the condensed water, hydration water, and strongly bounded water on the sulfonic acid group. In the present study, on the contrary to an expectation on this schematic, even the condensed water is found unfrozen when the membrane is cooled down to -50 degrees C, and a freezing begins when it is cooled down to -60 degrees C or lower. Two-thirds of the condensed water remains unfroten even at -80 degrees C which is attributed to the effect of nanospace where the water molecules are too short to construct the ice-like structure. The reduction of rotational motion of water is, on the other hand, commonly found for all the water species revealed via the calculation of the activation energies.