An electronic device on a plastic substrate, at least one side of the device being protected from reaction with or incorporation of moisture by a composite barrier. The composite barrier may contain, for example, multiple layers of transparent conductive oxide separated by one or more vacuum-evaporated in-situ polymerized organic layers, or may contain multiple barrier layers of transparent conductive oxide, transparent metal, or transparent conductive metal nitride, separated by at least one layer of organic dielectric polymer.