Process for the manufacture of .alpha.,.beta.-unsaturated N-substituted carboxylic acid amides of the general formula ##STR1## in which R.sup.1 represents H or CH.sub.3R.sup.2 represents H or CH.sub.3, andY represents a divalent straight-chain or branched organic radical having 2-30 carbon atoms, andR.sup.3 represents H or the radical of an amine of the formula --N(R.sup.4)(R.sup.5), in which R.sup.4 and R.sup.5 represent alkyl radicals having 1 to 4 carbon atoms,by reacting .beta.-substituted carboxylic acid amides of the formula ##STR2## in which Z represents OH or the radical R.sup.6 O--, in which R.sup.6 is an alkyl radical having 1 to 4 carbon atoms,with amines of the general formulaH.sub.2 N--(Y)--R.sub.3 IIIat temperatures in the range of 100.degree. to 200.degree. C., preferably 120.degree. to 175.degree. C., with the elimination of ammonia, and heating the resulting N-substituted .beta.-hydroxycarboxylic or .beta.-alkoxycarboxylic acid amides in the presence of catalysts, water or alcohol, respectively, being split off. The water is split off at temperatures of 100.degree.-250.degree. C. with acidic catalysts such as phosphoric acid, or basic catalysts such as sodium hydroxide, and alcohol is split off at 70.degree.-150.degree. C. with basic catalysts such as sodium or potassium hydroxide. The reaction product is separated by distillation, optionally in vacuo.