Isoxazole(isothiazole)-5-carboxamides of the formula ##STR1## where X is oxygen or sulfur,R.sup.1 is hydrogen, substituted or unsubstituted alkyl, alkoxy, substituted or unsubstituted cycloalkyl, a 5- or 6-membered heterocyclic radical having one or two heteroatoms selected from the group consisting of oxygen, sulfur and nitrogen, and which may be substituted, or substituted or unsubstituted phenyl, orR.sup.2 is formyl, 4,5-dihydrooxazol-2-yl or a radical of the formula COYR.sup.5 or CONR.sup.6 R.sup.7, whereY is oxygen or sulfur,R.sup.5 ishydrogen, substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, haloalkenyl, substituted or unsubstituted alkynyl,cycloalkyl,cycloalkenyl,substituted or unsubstituted phenyl,a 5- or 6-membered heterocyclic radical having one or two heteroatoms selected from the group consisting of oxygen, sulfur and nitrogen,cycloalkanimino, phthalimido, succinimido, or a radical ##STR2## R.sup.3 and R.sup.4 have the meanings defined herein, or their agriculturally acceptable salts possess herbicidal activity.