Cross-linked polymeric gels or films are prepared by dissolving in a suitable solvent a linear polymer or polymers at least one of which is predominantly (at least 80%) made from monomers containing pendant amidocarbonyl or oxycarbonyl groups. For the cross-linking reaction are present either hydroxyl groups, present as either pendant groups from the polymer, or as low molecular weight polyols; or amino groups, present as either pendant groups from the polymer, or as low molecular weight diamines or polyamines. Either no catalyst is present or a strongly acidic catalyst (which may also be a pendant group on a polymer) is used. The solvent is removed by coagulation and/or drying and the dry material is heat-cured, thus cross-linking and insolubilizing the polymer or polymers.