Production of pure N-dimethylacylamides having from two to four carbon atoms in the acyl radical by reaction of an excess of dimethylamine with an aliphatic carboxylic acid having two to four carbon atoms at elevated temperature and distillation of the N-dimethylacylamide formed, the distillation being carried out continuously in a column. Dimethylamine and the carboxylic acid in the molar ratio from 1.1:1 to 5:1 are introduced at from 80* to 220* C. and from 0.1 to 2 atmospheres in the absence of any catalyst into a mixture of N-dimethylacylamide and its carboxylic acid, the carboxylic acid content of the mixture corresponding at least to the amount of carboxylic acid present in the azeotropic mixture of the N-dimethylacylamide and its carboxylic acid. Ndimethylacylamides are used as solvents for polymers.