Barrier materials for reducing the permeability of plastic packaging materials are provided, characterized as containing at least about seven percent by weight amine nitrogen, or a total of at least about 17 percent amine nitrogen plus hydroxyl groups. The barrier materials exhibit oxygen permeability of less than about 1.5 cc-mil/100 in.sup.2 -day-atmosphere and a carbon dioxide permeability of less than about 15 cc-mil/100 in.sup.2 -day-atmosphere at 23.degree. C. and zero percent relative humidity. The barrier material can be formed from polyepoxide and polyamine. Optionally the polyamine may comprise prereacted polymeric resin formed from a polyepoxide and a polyamine. Multilayer packaging materials and multilayer containers including the polyamine-polyepoxide barrier material are part of the invention.