Compositions comprising a blend of two or more paper strengthening agents have improved stability compared with previously known paper strengthening agents. One component is a polymeric paper strengthening agent, preferably a wet strengthening agent. The other component is a stabilized polyacrylamide prepared by (1) reacting a first portion of glyoxal with a polyacrylamide having pendant amide groups to form a first reaction mixture comprising polyacrylamide; (2) adding an acid to the first reaction mixture to form a second reaction mixture having a reduced pH and comprising the polyacrylamide; and (3) adding a second portion of glyoxal to the second reaction mixture to form the stabilized polyacrylamide. If desired, an aldehyde scavenger can be included in one or more of step (1), step (2), step (3), or the stabilized polyacrylamide. Such compositions can be used to enhance the strength of paper, particularly the wet strength of paper.