Abstract: A method of obtaining aromatic tri- or tetracarboxylic acids characterized in that tri- or tetraalkylbenzenes or the derivatives thereof with a heteroatom in the side chain, are oxidized by oxygen or an oxygen-containing gas in the vapor phase in the presence of ammonia and water vapor at a molar ratio of the parent alkylbenzenes, oxygen or oxygen-containing gas, ammonia and water vapor equal to 1:2-100:5-40:30-100, respectively, on catalysts comprising vanadium oxides modified by the oxides of tin, titanium, bismuth or molybdenum at a molar ratio of vanadium oxides to the modifying oxides equal to 1:0.5-8 and a temperature of from 350.degree. to 440.degree. C, whereupon the resulting nitriles, imides, cyanimides or the mixtures thereof are subjected to acid or alkaline hydrolysis by 2-10 per cent aqueous solutions of acids or alkalis at a temperature of from 60.degree. to 100.degree. C.