The 50% increased permeability after annealing of semicrystalline poly(ethylene/vinylacetate) containing 3 mol % vinylacetate is linked to increased mobility in the amorphous phase, as identified by line-narrowing of H-1 wideline nuclear magnetic resonance (NMR) spectra and by reduced cross-polarization efficiency in (13) C NMR. Other morphological parameters, such as crystallinity, measured as 30 to 35% by differential scanning calorimetry (DSC) and NMR, are hardly changed by annealing. Small-angle X-ray scattering and NMR studies, using spin diffusion as well as T-1 rho and T-1 relaxation, detected only a small increase in crystallite thickness. The annealing-induced enhancement in segmental mobility in the amorphous regions corresponds to a temperature shift of about 10 K, from which an increase of the motional rate by a factor of 2 is estimated, and which can account for the enhancement in the permeability.