A skin- or hair-cleansing composition including a component (A), which is an aqueous gelling agent represented by general formula (1) described in the specification, and a component (B), which is an anionic surfactant, wherein the component (A) presents a viscosity of an aqueous solution containing 1 mass % of at 25° C. of 1,000 to 5,000 mPa·s and a clouding point of the aqueous solution containing 1 mass % of component (A) of 60° C. to 80° C., and has a weight average molecular weight of 10,000 to 30,000; a method for producing the aqueous gelling agent and a method for producing the skin- or hair-cleansing composition are provided.