Preparation of carboxylic acid amides

A method for making an amide of the formula ##STR9## wherein R.sub.1 is hydrogen or methyl, R.sub.4 is hydrogen, straight-chain or branched alkyl, or straight-chain or branched alkyl substituted by carboxy, alkoxycarbonyl, (alkyl)carbamoyl, sulfo, sulfoamido, or (alkyl)amino, and R.sub.3 is --AX, wherein A is --(CR.sub.5 R.sub.6).sub.n, phenylene, or naphthalene, R.sub.5 is hydrogen or alkyl having 1 to 6 carbon atoms, R.sub.6 is hydroxy or alkyl having 1 to 6 carbon atoms, X is hydrogen, carboxy, alkoxycarbonyl, (alkyl)carbamoyl, sulfo, sulfoamido, or (alkyl)amino and n is a whole number from 1 to 18 if X is other than (alkyl)amino or is a whole number from 2 to 18 if X is alkylamino, which method comprises reacting an ester of the formula ##STR10## wherein R.sub.2 is alkyl having 1 to 6 carbon atoms, with heating and under pressure, in a homogeneous phase in the presence of a catalytic concentration of protons, with an amine of the formula ##STR11## said amine being present in an amount which is stoichiometrically deficient up to an amount which is in small stoichiometric excess with respect to said ester.