Process for the preparation of 4-aminobut-2-enolide compounds of the formula comprising the reaction of a 4-alkoxyfuran-2 -one compound or 4-arylalkoxyfuran-2 -one compound of the formula with an amine of the formula in which R 1 is hydrogen, C 1-12 -alkyl, C 1-12 -haloalkyl, C 2-12 -alkenyl, C 2-12 -haloalkenyl, C 2-6 -alkynyl, C 3-8 -cycloalkyl, C 3-8 -cycloalkyl-C 1-6 -alkyl, C 3-8 -halocycloalkyl, C 1-12 -alkoxy, C 1-6 -alkyloxy-C 1-6 -alkyl, C 3-8 -halocycloalkyl-C 1-6 -alkyl or aryl-C 1-6 -alkyl; R 2 is C 1-12 -alkyl, or aryl-C 1-6 -alkyl, where aryl is to be understood as meaning an aromatic radical having 6 to 14 carbon atoms; and A is pyrid-2-yl, pyrid-4-yl or pyrid-3-yl, which is optionally substituted in the 6-position by F, Cl, Br, CH 3, CF 3, or OCF 3, is pyridazin-3-yl, which is optionally substituted in the 6-position by Cl or CH 3, is pyrazin-3-yl, 2-chloropyrazin-5-yl or is 1,3-thiazol-5-yl optionally substituted in the 2-position by Cl or CH 3, is pyrimidinyl, pyrazolyl, thiophenyl, oxazolyl, isoxazolyl, 1,2,4-oxadiazolyl, isothiazolyl, 1,2,4-triazolyl or 1,2,5-thiadiazolyl, which is optionally substituted by F, Cl, Br, CN, NO 2, C 1-4 -alkyl, C 1-3 -alkylthio C 1-3 -alkylsulphonyl, where each of the radicals C 1-4 -alkyl, C 1-3 -alkylthio and C 1-3 -alkylsulphonyl may be substituted by F and/or chlorine, or is a substituted heterocyclyl of the following formula in which X is halogen, C 1-12 -alkyl or C 1-12 -haloalkyl, and Y is halogen, C 1-12 -alkyl, C 1-12 -haloalkyl, C 1-12 -haloalkoxy, azido or CN; in the presence of a Brønsted acid, wherein the Brønsted acid is selected from the group consisting of phosphoric acid, sulphuric acid, hydrochloric acid, hydrobromic acid, hydrofluoric acid, potassium hydrogensulphate, trifluoroacetic acid, methanesulphonic acid and p-toluenesulphonic acid, and wherein the molar ratio of Brønsted acid to the amine of the formula is in the range of 10:0.6-1:1.5. R 1 is hydrogen, C 1-12 -alkyl, C 1-12 -haloalkyl, C 2-12 -alkenyl, C 2-12 -haloalkenyl, C 2-6 -alkynyl, C 3-8 -cycloalkyl, C 3-8 -cycloalkyl-C 1-6 -alkyl, C 3-8 -halocycloalkyl, C 1-12 -alkoxy, C 1-6 -alkyloxy-C 1-6 -alkyl, C 3-8 -halocycloalkyl-C 1-6 -alkyl or aryl-C 1-6 -alkyl; R 2 is C 1-12 -alkyl, or aryl-C 1-6 -alkyl, where aryl is to be understood as meaning an aromatic radical having 6 to 14 carbon atoms; and A is pyrid-2-yl, pyrid-4-yl or pyrid-3-yl, which is optionally substituted in the 6-position by F, Cl, Br, CH 3, CF 3, or OCF 3, is pyridazin-3-yl, which is optionally substituted in the 6-position by Cl or CH 3, is pyrazin-3-yl, 2-chloropyrazin-5-yl or is 1,3-thiazol-5-yl optionally substituted in the 2-position by Cl or CH 3, is pyrimidinyl, pyrazolyl, thiophenyl, oxazolyl, isoxazolyl, 1,2,4-oxadiazolyl, isothiazolyl, 1,2,4-triazolyl or 1,2,5-thiadiazolyl, which is optionally substituted by F, Cl, Br, CN, NO 2, C 1-4 -alkyl, C 1-3 -alkylthio C 1-3 -alkylsulphonyl, where each of the radicals C 1-4 -alkyl, C 1-3 -alkylthio and C 1-3 -alkylsulphonyl may be substituted by F and/or chlorine, or is a substituted heterocyclyl of the following formula X is halogen, C 1-12 -alkyl or C 1-12 -haloalkyl, and Y is halogen, C 1-12 -alkyl, C 1-12 -haloalkyl, C 1-12 -haloalkoxy, azido or CN;