The crystalline structure, dynamics, and gas transport properties (i.e., the gas permeability, gas diffusion coefficient, and gas solubility coefficient) of poly(tetrafluoroethylene-co-perfluoroethylvinylether) (PFA) membranes were systematically investigated via differential scanning calorimetry, wide/small/ultra-small-angle X-ray scattering, and quasielastic neutron scattering measurements. We evaluated the gas transport properties using a constant-volume/variable-pressure method. The gas permeability and the gas diffusion coefficient decreased with increasing crystallinity of the PFA membranes at crystallinities below 32%. However, in membranes with a crystallinity of 32% or greater, these parameters depended on the characteristics of the gas molecules, such as their kinetic diameter. The so-called long spacing period and the thickness of the crystalline/amorphous regions increased with crystallinity according to the small/ultra-small-angle X-ray scattering results. Furthermore, the quasielastic neutron scattering measurements indicated that the scattering law was well fitted to a sum of narrow and broad Lorentzian components. In particular, the narrow components, that is, the local motion of amorphous components and side chains, increased with crystallinity. These results suggest that large gas molecules could pass through the PFA membranes, assisted by the motion in the amorphous region. V C 2017 Wiley Periodicals, Inc. J.Appl. Polym. Sci. 2018, 135, 45665.