3-Phenylisoxazoline-5-carboxamides or 3-phenylisoxazoline-5-thioamides of the formula or salts thereof in which R 1 and R 2 independently of one another are each hydrogen, fluorine, chlorine, bromine, iodine, cyano, or (C 1 -C 4)-alkyl or (C 1 -C 4)-alkoxy substituted by in each case m radicals from the group consisting of fluorine, chlorine, bromine, iodine and cyano, or R 1 and R 2 together with the carbon atom to which they are attached form a saturated, partially or fully unsaturated three-, four- or 5-membered ring which is constructed of q carbon atoms and p oxygen atoms; R 3 is fluorine, chlorine, cyano, (C 1 -C 3)-alkylcarbonyloxy or S n R 5, or (C 1 -C 6)-alkyl, (C 3 -C 6) -cycloalkyl, (C 2 -C 6) -alkenyl or (C 2 -C 6)-alkynyl substituted by in each case m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano, (C 1 -C 4)-alkoxy and hydroxy, or (C 1 -C 6) -alkylcarbonyl, (C 2 -C 6) -alkenylcarbonyl or (C 3 -C 6)-cycloalkylcarbonyl substituted by in each case m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano and (C 1 -C 6)-alkoxy; R 4 is hydrogen, cyano, or (C 1 -C 8)-alkyl or (C 3 -C 8)-cycloalkyl substituted by in each case m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano, hydroxy and (C 1 -C 6)-alkoxy; A is a bond or a divalent unit from the group consisting of R 10, R 11, R 12, R 13, R 14 and R 15 are each independently of one another hydrogen, fluorine, chlorine, bromine, iodine, hydroxy, cyano, CO 2 R 8, CONR 6 R 8, R 5, or (C 1 -C 6)-alkyl, (C 3 -C 5)-cycloalkyl, (C 2 -C 6) -alkenyl, (C 2 -C 6)-alkynyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, iodine, hydroxy and cyano; or (C 1 -C 6)-alkoxy, (C 3 -C 6) -cycloalkoxy, (C 2 -C 6)-alkenyloxy or (C 2 -C 6)-alkynyloxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano and (C 1 -C 2)-alkoxy, Y is oxygen or sulfur; X is hydrogen, cyano, hydroxy, X 1, or (C 1 -C 12) -alkyl, (C 3 -C 8) -cycloalkyl, (C 2 -C 12) -alkenyl or (C 2 -C 12) -alkynyl substituted by in each case m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano, hydroxy, OR 7, X 1, OX 1, NHX 1, S n R 5, SO 2 NR 6 R 7, SO 2 NR 6 R 8, CO 2 R 8, CONR 6 R 8, COR 6, CONR 8 SO 2 R 5, NR 6 R 8, NR 6 COR 8, NR 6 CONR 8 R 8, NR 6 CO 2 R 8, NR 6 SO 2 R 8, NR 6 SO 2 NR 6 R 8, OCONR 6 R 8, OCSNR 6 R 8, POR 9 R 9 and C (R 6) =NOR 8, or X, A and R 4 together with the nitrogen atom to which they are attached form a saturated, partially or fully unsaturated five-, six- or seven-membered ring which, in addition to this nitrogen atom, contains k carbon atoms, n oxygen atoms, p sulphur atoms and p elements from the group consisting of NR 7 and NCOR 7 as ring atoms, where a carbon atom carries p oxo groups; X 1 is a 5- or 6-membered saturated, partially unsaturated, fully unsaturated or aromatic ring which is constructed of r carbon atoms, s nitrogen atoms, n sulphur atoms and n oxygen atoms and which is substituted by n radicals from the group consisting of R 6, R 6a, R 8 and R 9; X 2, X 4 and X 6 independently of one another are each hydrogen, fluorine, chlorine, bromine, iodine, cyano, nitro, or (C 1 -C 4)-alkyl, (C 3 -C 5) -cycloalkyl, (C 2 -C 4)-alkenyl, (C 2 -C 4)-alkynyl, (C 1 -C 4)-alkoxy, (C 2 -C 4) -alkenyloxy, (C 2 -C 4)-alkynyloxy or (C 1 -C 4)-alkylcarbonyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano and (C 1 -C 4)-alkoxy; X 3 is fluorine, chlorine, bromine, iodine, hydroxy, cyano, nitro, SF 5, CONR 8 SO 2 R 5, CONR 6 R 8, COR 6, CO 2 R 8, CONR 6 R 8, C(R 6)=NOR 8, NR 6 COR 8, NR 6 CONR 8 R 8, NR 6 CO 2 R 8, NR 6 SO 2 R 8, NR 6 SO 2 NR 6 R 8, OCONR 6 R 8, OSO 2 R 5, R 5, S n R 5, SO 2 NR 6 R 8, OSO 2 NR 6 R 8, or (C 1 -C 6)-alkyl, (C 3 -C 5) -cycloalkyl, (C 2 -C 6) -alkenyl, (C 2 -C 6)-alkynyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, iodine, hydroxy and cyano, or (C 1 -C 6)-alkoxy, (C 3 -C 6) -cycloalkoxy, (C 2 -C 6)-alkenyloxy or (C 2 -C 6)-alkynyloxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano and (C 1 -C 2)-alkoxy, X 5 is hydrogen or X 3; R 5 is (C 1 -C 6)-alkyl or (C 3 -C 6)-cycloalkyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, iodine, cyano and hydroxy; R 6 is hydrogen or R 5; R 6a is fluorine, chlorine, bromine, iodine, cyano, hydroxy, S n R 5 or (C 1 -C 6) -alkoxy, (C 2 -C 6) -alkenyloxy or (C 3 -C 6)-alkynyloxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, cyano and (C 1 -C 2)-alkoxy; R 7 is hydrogen or (C 1 -C 6)-alkyl, (C 3 -C 6) -cycloalkyl, (C 2 -C 4)-alkenyl or (C 2 -C 4)-alkynyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, cyano and (C 1 -C 2)-alkoxy; R 8 is R 7; R 9 is (C 1 -C 3)-alkyl or (C 1 -C 3)-alkoxy; k is 3, 4, 5 or 6; m is 0, 1, 2, 3, 4 or 5; n is 0, 1 or 2; p is 0 or 1; q is 3, 4 or 5; r is 1, 2, 3, 4 or 5; s is 0, 1, 2, 3 or 4; with the proviso that X 3 and X 4 are not both substituted or unsubstituted alkoxy.