Abstract: A method of isomerizing alkylbenzenes, in particular xylenes. The method is based on the application of a catalyst which comprises an inorganic oxide support containing at least one mixed oxide compound of SiO.sub.2 and Al.sub.2 O.sub.3 in any proportion, and performing the isomerization at a temperature between 150.degree. and 300.degree. C. under a pressure ranging from about atmospheric to a few atmospheres. The catalyst is produced by reaction of the support with an aluminum alkyl compound of the type AlR.sub.y X.sub.3-y, wherein R=CH.sub.3, C.sub.2 H.sub.5 or C.sub.3 H.sub.7, y=1 or 2 and X=Cl, preferably Al(C.sub.2 H.sub.5)Cl.sub.2. The support may be impregnated with platinum and/or rhenium. Characteristic features of this method are that the isomerization process can be run without any promotor, and that isomerization of xylene under moderate conditions yields a high degree of conversion and high selectivity.