To obtain a permanent wave-treating agent composition capable of imparting excellent wave while preventing the damage to the hair.

This permanent wave-treating agent composition contains (A) thioglycolic acid or a salt thereof, and/or cysteine, N-acetylcysteine or a salt thereof, and (B) an arginine derivative represented by general formula (1) (wherein, R1 is a 6-24C alkyl group or alkenyl group) or a salt thereof.