A process for producing l,2-benzisoxazole-3-methanesulfonamide which comprises using 4-hydroxycoumarin as a starting material and water and 1,2-dichloroethane as solvents to produce the target compound without isolating intermediates in the form of a solid and an industrially useful process for producing 1,2-benzisoxazole-3 -acetic acid, characterized by reacting 4-hydroxycoumarin with hydroxylamine in water.