preparing acidic alkyl phosphate which is solid at room temperatures; and

gradually adding said prepared acidic alkyl phosphate with stirring to an aqueous solution containing potassium hydroxide and Component A in an amount sufficient to partially neutralize said acidic alkyl phosphate, said Component A consisting of one or more selected from the group consisting of alkylene oxide adducts of aliphatic monohydric alcohol, alkylene oxide adducts of substituted aromatic monohydric alcohol, alkylene oxide adducts of aliphatic amine, organic sulfonates, higher fatty acid salts, salts of acidic alkyl phosphates which are liquid at room temperatures, alkenyl phosphate salts, alkyl(poly)oxyalkylene phosphate salts and alkenyl(poly)oxyalkylene phosphate salts, thereby obtaining 0.1-10 weight % low concentration aqueous solution of agent for processing synthetic fibers containing potassium alkyl phosphate which is solid at room temperatures and said Component A.