Novel films, and processes for making them, are provided. The films are characterized by the inclusion of a layer of vinylidene chloride copolymer between at least two other layers which contain ethylene vinyl acetate, and optionally linear low density polyethylene. The films may be unoriented or oriented. Oriented films may optionally be cross-linked. The novel process of making the cross-linked films includes the step of cross-linking the film after assembly of the vinylidene chloride copolymer layer into the structure.