A method for the production of a stable aqueous acrylonitrile polymer which comprises polymerizing acrylonitrile alone or in a monomer mixture comprising more than 60% by weight of acrylonitrile and as another component, at least one other ethylenically unsaturated compound, under stirring at a temperature higher than 120.degree. C. and at least autogeneous pressure, in an aqueous system consisting essentially of water in an amount of 45 to 95% by weight based on the total weight of water and monomer(s), to thereby introduce at least 2.times.10.sup.-5 mol per gram polymer of sulfonic acid groups or salts thereof and/or carboxylic groups or salts thereof into the resulting polymer, whereby an aqueous dispersion system comprising fine droplets of the polymer in substantially molten state is formed, and then cooling said aqueous dispersion system under stirring so that said polymer droplets may not gather together to form aggregates, said cooling of said aqueous dispersion system being to a temperature less than 100.degree. C. while maintaining said system at a pressure higher than the autogenous pressure.