The invention relates to glyoxalated N-vinylamine. Specifically, the present invention is directed to compositions comprising a cellulose reactive functionalized polyvinylamine first adduct, compositions comprising combinations of the cellulose reactive functionalized polyvinylamine first adduct and cellulose reactive functionalized polyvinylamide second adduct, methods for preparing first adduct and second adduct blends and finally methods of increasing the wet or dry strength of paper by incorporation into the paper furnish or coating a paper or board with said adducts.