The permeability, diffusion, and solubility constants of helium, argon, and ethane have been measured in a series of linear polyethylene films which had been subjected (1) to various rates of cooling from the melt and (2) to subsequent annealing near the melting temperature. While solubility constants of argon and ethane showed the normal variation with amorphous content of the polymer irrespective of thermal history, helium solubility constants appeared to be anomalously high and strongly dependent on thermal history. The presence of voids or defects within the crystalline phase has been postulated to account for this behavior of helium; argon and ethane being excluded from these defects because of their size. Anomalous helium diffusion constants were also observed which have been satisfactorily explained in terms of a slow diffusion of gas into these intracrystalline defects.The monatonic decrease in geometric diffusional impedance with increasing amorphous content of the polymer has again been observed in films directly cooled from the melt. However, upon annealing these films at elevated temperatures the impedance decreases markedly, despite an increase in crystallinity, suggesting the formation of thicker lamellas with a high concentration of intralamellar imperfections in a manner similar to that observed in annealing polyethylene single crystals.The apparent activation energies for diffusion of argon and ethane were essentially constant irrespective of thermal history. This suggests the so called ``chain immobilization factor'' is not due to restricted chain mobility in the amorphous polymer, but is rather a penetrant‐size‐dependent impedance to diffusion arising from the near‐molecular dimensions of the amorphous channels in the polymer.