To avoid gellation in the preparation of aldehyde-substituted amide polymers, substituted amide monomer is reacted with a polyaldehyde and, simultaneously and/orsub- sequently, polymerized with at least one other monomer to provide polymer containing free aldehyde groups and in which the polyaldehyde is predominantly mono-functionally bonded to the polymer. The polymer may be crosslinked by added crosslinker or is self-crosslinkable when it contains unreacted amide groups. Preferred reactants are acrylamide or methacrylamide, glyoxal and acrylic or methacrylic acid esters. The polymers may be used as binders in the manufacture of paper and nonwoven fabrics.