A tissue-adhesive polymer comprising vinyl pyrrolidone-derived units and acrylate-derived units containing at least one ester group and a tissue-reactive group. Also provided are freeze-dried compositions containing said polymer which may provide a tissue-contacting layer in tissue-adhesive articles, for example sheets having one or more layers. The freeze-dried compositions may be prepared by freeze-drying solutions of the tissue-adhesive polymer in dimethyl sulfoxide (DMSO). Alternatively, the polymer may be in hydrogels with tissue-sealing properties wherein the hydrogel further comprises nucleophilic groups. In other embodiments are the monomer mono(2-acryloyloxyethyl)succinate (MAES) and mono(2-acryloyloxyethyl)succinate N-hydroxysuccinimide ester (MAES-NHS) and their use as the acrylate-derived unit in the tissue-adhesive polymer.