3-Phenylisoxazoline-5-carboxamides and -5-thioamides of the general formula and the agrochemically acceptable salts thereof in which R 1 and R 2 independently of one another each represent hydrogen, fluorine, chlorine or cyano, or represent (C 1 -C 3)-alkyl or (C 1 -C 3)-alkoxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine and cyano; R 3 represents (C 1 -C 4)-alkyl, (C 3 -C 5)-cycloalkyl, (C 2 -C 4)-alkenyl, (C 2 -C 4)-alkynyl or (C 1 -C 4)-alkoxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, cyano, (C 1 -C 4)-alkoxy and hydroxy; R 4 represents hydrogen, or represents (C 1 -C 12)-alkyl, (C 3 -C 7)-cycloalkyl, (C 3 -C 7)-cycloalkyl- (C 1 -C 8)-alkyl, (C 2 -C 6)-alkenyl, (C 5 -C 6)-cycloalkenyl or (C 2 -C 8)-alkynyl, each of which is substituted by m radicals from the group consisting of halogen, cyano, (C 1 -C 6)-alkoxy, hydroxy and aryl; Y represents oxygen or sulfur; W represents oxygen or sulfur; Z represents a fully saturated or partially saturated furan ring which is substituted by k radicals from the group R 5, where the arrow in each case denotes a bond to the group C=W of the formula; R 5 represents fluorine, chlorine, cyano or CO 2 R 7, or represents (C 1 -C 2)-alkyl or (C 1 -C 2)-alkoxy, each of which is substituted by m radicals from the group consisting of fluorine and chlorine; X 2, X 4 and X 6 independently of one another each represent hydrogen, fluorine, chlorine, bromine or cyano, or represent (C 1 -C 2)-alkyl, in each case substituted by m radicals from the group consisting of fluorine, chlorine, bromine and (C 1 -C 2)-alkoxy; X 3 and X 5 independently of one another represent hydrogen, fluorine, chlorine, bromine, iodine, hydroxy, cyano, nitro, S n R 6 or CO 2 R 7, or represent (C 1 -C 3)-alkyl, (C 1 -C 3)-alkoxy, (C 3 -C 4)-cycloalkyl, (C 2 -C 3)-alkenyl or (C 2 -C 3)-alkynyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine and bromine; R 6 represents (C 1 -C 2)-alkyl or (C 3 -C 4)-cycloalkyl, each of which is substituted by m radicals from the group consisting of fluorine and chlorine; R 7 represents hydrogen, or represents (C 1 -C 3)-alkyl or (C 3 -C 5)-cycloalkyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine and (C 1 -C 2)-alkoxy; k is the running number 0, 1 or 2; m is the running number 0, 1, 2, 3, 4 or 5; and n is the running number 0, 1 or 2. R 1 and R 2 independently of one another each represent hydrogen, fluorine, chlorine or cyano, or represent (C 1 -C 3)-alkyl or (C 1 -C 3)-alkoxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine and cyano; R 3 represents (C 1 -C 4)-alkyl, (C 3 -C 5)-cycloalkyl, (C 2 -C 4)-alkenyl, (C 2 -C 4)-alkynyl or (C 1 -C 4)-alkoxy, each of which is substituted by m radicals from the group consisting of fluorine, chlorine, bromine, cyano, (C 1 -C 4)-alkoxy and hydroxy; R 4 represents hydrogen, or represents (C 1 -C 12)-alkyl, (C 3 -C 7)-cycloalkyl, (C 3 -C 7)-cycloalkyl- (C 1 -C 8)-alkyl, (C 2 -C 6)-alkenyl, (C 5 -C 6)-cycloalkenyl or (C 2 -C 8)-alkynyl, each of which is substituted by m radicals from the group consisting of halogen, cyano, (C 1 -C 6)-alkoxy, hydroxy and aryl; Y represents oxygen or sulfur; W represents oxygen or sulfur; Z represents a fully saturated or partially saturated furan ring which is substituted by k radicals from the group R 5, where the arrow in each case denotes a bond to the group C=W of the formula; R 5 represents fluorine, chlorine, cyano or CO 2 R 7, or represents (C 1 -C 2)-alkyl or (C 1 -C 2)-alkoxy, each of which is substituted by m radicals from the group consisting of fluorine and chlorine; X 2, X 4 and X 6 independently of one another each represent hydrogen, fluorine, chlorine, bromine or cyano, or represent (C 1 -C 2)-alkyl, in each case substituted by m radicals from the group consisting of fluorine, chlorine, bromine and (C 1 -C 2)-alkoxy; X 3 and X 5 independently of one another represent hydrogen, fluorine, chlorine, bromine, iodine, hydroxy, cyano, nitro, S n R 6 or CO 2 R 7, or represent (C 1 -C 3)-alkyl, (C 1 -C 3)-alkoxy, (C 3 -C 4)-cycloalkyl, (C 2 -C 3)-alkenyl or (C 2 -C 3)-alkynyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine and bromine; R 6 represents (C 1 -C 2)-alkyl or (C 3 -C 4)-cycloalkyl, each of which is substituted by m radicals from the group consisting of fluorine and chlorine; R 7 represents hydrogen, or represents (C 1 -C 3)-alkyl or (C 3 -C 5)-cycloalkyl, each of which is substituted by m radicals from the group consisting of fluorine, chlorine and (C 1 -C 2)-alkoxy; k is the running number 0, 1 or 2; m is the running number 0, 1, 2, 3, 4 or 5; and n is the running number 0, 1 or 2.