This invention relates to a process for the preparation of acid amides having the formula (I) or their salts ##STR1## wherein R.sup.1 is hydrogen or an easily removable ester-forming or salt-forming group, preferably a trialkylamine, trialkylsilyl, trichloroethyl, acetoxymethyl, phenacyl, substituted phenacyl, substituted phenyl or benzyl group,R.sup.2 is hydrogen, alkyl group, alkenyl group, alkyl group having an aryl or heterocyclic (preferably furyl or thienyl) - substituent, an aryl group having an alkyl substituent (preferably xylyl), or an aryl, aralkyl or heterocyclic group (preferably a phenyl, thienyl, or furyl group) which can have one or more substituents,R.sup.3 is hydrogen, or substituted or unsubstituted aryl, alkyl, cycloalkyl or aralkyl group, andX is a group of one of the formulae ##STR2## according to the invention an amine of the formula (II), ##STR3## wherein R.sup.4 is an easily removable ester-forming group, preferably a trialkylamino, trialkylsilyl, trichloroethyl, acetoxymethyl, phenacyl, substituted phenacyl, substituted phenyl or benzyl group, or a salt formed preferably with an alkali metal or a trialkylamine, is acylated with an ester of the formula (III), ##STR4## wherein R.sup.5 is a substituted or unsubstituted aryl, alkyl, cycloalkyl or aralkyl group, and, if desired, substituents R.sup.4 and/or R.sup.5 of the obtained product can be split off, and/or, if desired, the obtained product is converted into its salt or a salt is converted into the free acid.