A novel process for preparing amidoalkanesulfonic acids represented by formula (3) and their derivatives by reacting a nitrile compound (1) with beta-hydroxyalkanesulfonic acid or its derivative (2) in conc. sulfuric acid. Of the compounds of the formula (3) and their derivatives, unsaturated amidophenyl-substitued alkanesulfonic acids represented by formula (4) and their derivatives, particularly, 2-acrylamido-2-phenylpropanesulfonic acid and its derivatives are copolymerized with other monomers to provide useful materials such as copolymer-coated solid substances, copolymer emulsions, and pigment-dispersing agent.