A process for preparing a composition comprising at least one unsaturated carboxylic acid of the general formula or a salt thereof, in which R 1 is hydrogen, linear or branched C 1 -C 24 -alkyl, linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, unsubstituted C 5 -C 12 cycloalkyl or C 5 -C 12 -cycloalkyl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals or unsubstituted aryl or aryl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals, R 2 is hydrogen, linear or branched C 1 -C 24 -alkyl or linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, or R 1 and R 2 together with the carbon atom to which they are bonded are unsubstituted C 5 -C 7 -cycloalkyl or are C 5 -C 7 -cycloalkyl bearing 1, 2 or 3 linear or branched C 1 -C 6 -alkyl radicals, in which an allyl alcohol selected from compounds of the general formulae (II.1) and (II.2) is subjected to a carbonylation by reaction with carbon monoxide in the presence of a transition metal catalyst comprising at least one metal of groups 8, 9 and 10 of the Periodic Table of the Elements, wherein the reaction is additionally effected in the presence of at least one organic phosphorus compound as ligand and in the presence of a substoichiometric amount, based on the allyl alcohol, of a compound A) selected from anhydrides of aliphatic C 1 -C 12 -monocarboxylic acids, anhydrides of aliphatic C 4 -C 20 -dicarboxylic acids, anhydrides of cycloaliphatic C 7 -C 20 -dicarboxylic acids, anhydrides of aromatic C 8 -C 20 -dicarboxylic acids and acylated allyl alcohols of the formulae (III.1) and (III.2) in which R 3 is hydrogen, linear or branched C 1 -C 24 -alkyl, linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, unsubstituted C 5 -C 12 -cycloalkyl or C 5 -C 12 -cycloalkyl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals or unsubstituted aryl or aryl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals, R 4 is hydrogen, linear or branched C 1 -C 24 -alkyl or linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, or R 3 and R 4 together with the carbon atom to which they are bonded are unsubstituted C 5 -C 7 -cycloalkyl or are C 5 -C 7 -cycloalkyl bearing 1, 2 or 3 linear or branched C 1 -C 6 -alkyl radicals, R 5 is C 1 -C 5 -alkyl, and wherein the reaction is effected at a temperature of not more than 100°C; or in which an allyl alcohol selected from compounds of the general formulae (II.1) and (II.2) is subjected to a carbonylation by reaction with carbon monoxide in the presence of a transition metal catalyst comprising at least one metal of groups 8, 9 and 10 of the Periodic Table of the Elements, wherein the reaction is additionally effected in the presence of at least one organic phosphorus compound as ligand and in the presence of a substoichiometric amount, based on the allyl alcohol, of a compound B) in which R 10 and R 11, independently of one another, are C 1 -C 6 -alkyl, C 1 -C 6 -fluoroalkyl or phenyl which is unsubstituted or substituted by a substituent selected from bromo, nitro and C 1 -C 4 -alkyl; and wherein the reaction is effected at a temperature of not more than 100°C. R 1 is hydrogen, linear or branched C 1 -C 24 -alkyl, linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, unsubstituted C 5 -C 12 cycloalkyl or C 5 -C 12 -cycloalkyl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals or unsubstituted aryl or aryl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals, R 2 is hydrogen, linear or branched C 1 -C 24 -alkyl or linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, or R 1 and R 2 together with the carbon atom to which they are bonded are unsubstituted C 5 -C 7 -cycloalkyl or are C 5 -C 7 -cycloalkyl bearing 1, 2 or 3 linear or branched C 1 -C 6 -alkyl radicals, in which an allyl alcohol selected from compounds of the general formulae (II.1) and (II.2) R 3 is hydrogen, linear or branched C 1 -C 24 -alkyl, linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, unsubstituted C 5 -C 12 -cycloalkyl or C 5 -C 12 -cycloalkyl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals or unsubstituted aryl or aryl substituted by 1, 2 or 3 C 1 -C 6 -alkyl radicals, R 4 is hydrogen, linear or branched C 1 -C 24 -alkyl or linear or branched C 2 -C 24 -alkenyl having 1, 2, 3 or more than 3 C-C double bonds, or R 3 and R 4 together with the carbon atom to which they are bonded are unsubstituted C 5 -C 7 -cycloalkyl or are C 5 -C 7 -cycloalkyl bearing 1, 2 or 3 linear or branched C 1 -C 6 -alkyl radicals, R 5 is C 1 -C 5 -alkyl,