Local molecular motions of four homologous series of poly[oxy(alkylsulfonyl)ethylene]s such as poly[oxy(ethylsulfonylmethyl)ethylene], poly[oxy(propylsulfonylmethyl)ethylene], poly[oxy(butylsulfonylmethyl)ethylene], and poly[oxy(pentylsulfonylmethyl)ethylene] were correlated with their oxygen permeability in conjunction with their side chains varying from ethyl, n-propyl, n-butyl, to n-pentyl. To characterize and evaluate the local molecular motions, measurements of proton rotating-frame spin-lattice relaxation time, T-1 rho, over the temperature range 140-400 K were made. Then, the corresponding correlation times, tau (c)'s, were determined from fitting the relaxation data, and the activation energies, E-a, obeying the Arrhenius relation with tau (c), were accordingly obtained. The results of tau (c) and E-a fog the poly(oxyethylene)s were consistent with; their oxygen permeability coefficient where the slower local motion due to the shorter side chains imparted a lower oxygen permeability as in poly[oxy(ethylsulfonylmethyl)ethylene] and vice versa as in poly[oxy(pentylsulfonylmethyl)ethylene]. This was attributed to the fact that the longer side chains as in poly[oxy(pentylsulfonylmethyl)ethylene] pushed the neighboring chains further apart and decreased the restriction to the backbone chain motions, making them more locally mobile. This faster local motion in turn resulted in the higher oxygen permeation, while the slower local motion resulted in the higher barrier nature. The local molecular mobility evaluated by tau (c) and E-a was found to be another crucial factor governing the gas permeability of poly(oxyethylene)s.