An analysis of the diffusion of oxygen and carbon dioxide through linear low density polyethylene (LLDPE) subjected to longitudinal and transversal induced stretching in the ratio 2:1, is presented in this paper. The relaxation behavior of two coextruded LLDPE films prepared from copolymers of ethylene-1-octene is reported as well. The spectra, expressed in terms of loss tan delta, present a gamma relaxation shifted 5 degrees C to 10 degrees C in the LLDPE1 with respect to the LLDPE2 when the stretching was longitudinal. This relaxation is lower in intensity than the one exhibited for conventional low-density polyethylene of the same crystallinity. Increasing the temperature order, a beta relaxation process appears as an ostensible shoulder of the first of two relaxation processes, called alpha’ and alpha ", detected in the alpha region. The beta relaxation, which is believed to be produced by motion taking place in the amorphous and interfacial regions, appears as two overlapping peaks centered at -36 degrees C and -30 degrees C for a longitudinal stretching and at -34 degrees C and -28 degrees C for a transversal stretching at 1 Hz. In relation to this fact, we observed a slight increase in the T-alpha of the LLDPE2 with respect to the LLDPE1, which is greater in the transversally stretched polymers than in the longitudinal ones. The values of the activation energy corresponding to the second peak of the beta relaxation were obtained for the films subjected to stretching in longitudinal and transversal directions to the processing orientation. The study of the diffusional characteristics of oxygen and carbon dioxide through the films shows the temperature is related to the region for which the alpha processes are given. An anomalous behavior of the diffusion coefficient with the temperature is observed suggesting general movements around the amorphous segments and crystalline entities. The increase with the temperature of both parameters (diffusion and permeability) can be attributed to a change in the gas solubility. This increase is greater for CO2 than for O-2, which we interpret as a plastificant effect of the CO2. Finally, the activation energies from diffusion coefficient and permeability are analyzed in terms of Arrhenius. The results show that the temperature dependence of the diffusive parameters may not be a simply activated process as a consequence of the fact that the diffusional characteristics of the films depend on their morphology which, in turn, is changing with temperature. Little changes are observed when the films are subjected to any kind of stretching. In this sense, we think that the orientation by tensile drawing will decrease the conformational entropy involved in melting processes and, as a consequence, will reduce both the permeability and the apparent diffusion coefficients.