The relaxation behaviour of coextruded linear low-density polyethylene (LLDPE) films, prepared from copolymers of ethylene-1-octene, is reported. The spectra, expressed in terms of loss tan delta, present a gamma relaxation of lower intensity than that exhibited for conventional low density polyethylene of the same crystallinity, followed, with increasing temperature, by a beta relaxation process that appears as an ostensible shoulder of the first of two relaxation processes, denoted by alpha’ and alpha", detected in the alpha region. The beta relaxation, which is believed to be produced by motions taking place in the amorphous and interfacial. regions, appears as a well developed peak when the results are expressed in terms of the loss relaxation modulus. Whereas the alpha’ relaxation is believed to be associated with motions in which the crystalline entities intervene, the alpha" peak seems to be related to the crystallites thickening. The study of the characteristics of CO2 diffusion through the films shows that the permeability coefficient undergoes a significant increase between 27 and similar to 52 degrees C, followed by a plateau in which the permeability remains nearly constant. The permeability of oxygen follows similar trends, although the changes of this parameter with temperature are less ostensible. Gas diffusion through the films may not be a simple activated process since it seems to be governed by complicated molecular motions involving crystalline entities.