A composition includes water; at least one hydrophilic polymer containing at least two groups which are independently the same or different a primary amine group or a secondary amine group and at least one saccharide containing a reducible function as described above. The hydrophilic polymer and the saccharide are mixed to form a reaction mixture and reacted to increase the viscosity of the reaction mixture. The reaction is then substantially terminated by reducing the pH of the composition. A method of increasing the strength of a cellulosic pulp product includes the steps of: contacting wet cellulosic pulp with a composition comprising (i) at least one hydrophilic polymer containing at least two groups which are independently the same or different a primary amine group or a secondary amine group and at least one saccharide containing a reducible function, the hydrophilic polymer and the saccharide of the composition having been reacted in a crosslinking reaction prior to contacting the composition with the cellulosic pulp product to increase the viscosity the composition; and, after contacting the cellulosic pulp with the composition, causing the crosslinking reaction between the hydrophilic polymer and the saccharide of the composition to proceed further.