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Two ethylene‐vinyl acetate (EVA) resins with 19% (EVA19) and 28% (EVA28) of vinyl groups were used as compatibilizers for nanocomposites of high‐density polyethylene (HDPE) and nanoclays. Two nanoclays were also used, one with a nonpolar surfactant (C15A) and another with a polar surfactant (C30B). The HDPE/EVA19/C15A formed an intercalated structure, while the HDPE/EVA28/C30B had surfactant loss. Blown films of these compositions were produced. A two‐phase morphology made of HDPE and EVA/nanoclay particles was observed, which was responsible for the increase in water vapor and oxygen permeability rates of the films. The elastic modulus E along the transverse direction of the films was higher than along the machine direction due to preserved orientation given by the spiral die; the lamellae orientation was measured by small‐angle X‐rays diffraction. The highest E was observed in the HDPE/EVA19/C15A film due to stronger interactions. The long period of the HDPE lamellas was not affected by the presence of the EVA and nanoclay. A model was proposed to explain the improvement in elastic modulus due to the processing conditions and components' interactions. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010 [ABSTRACT FROM AUTHOR]