The mechanical relaxation spectra of co-extruded linear low-density polyethylene (LLDPE) films, prepared from copolymers of ethylene and 1-octene, were measured in parallel and transverse directions to the processing orientation. Both the gamma- and beta-relaxations do not show a noticeable dependence on the direction in which the measurements were performed. However, whereas the alpha-relaxation in the measurements performed in the parallel direction appears as two peaks, in order of increasing temperature, which were denoted as alpha’ and alpha ", the measurements carried out in the transverse direction only exhibit the alpha’-peak. The influence of tensile drawing on the permeability of co-extruded LLDPE films to oxygen and carbon dioxide was investigated by electrochemical techniques over the range of temperatures where the alpha’-relaxation process is located. In general, the permeability coefficients do not show a significant dependence on the drawing direction in the temperature interval corresponding to the low temperature region of the alpha’-peak. In this high-temperature zone, the values of the permeability coefficient for O-2 and CO2 through the oriented films after tensile drawing are significantly lower than those obtained for these gases through undrawn coextruded LLDPE films. The diffusion coefficients do not show a definite dependence on tensile drawing.