The invention concerns the use of a catalyst comprising at least one zeolite having a mazzite type structure in its acid form, the catalytic properties of the catalyst having been modified by depositing, on the external surface of the crystals, at least one metal selected from metals from group IIa of the periodic classification of the elements, such as Be, Mg, Ca, Sr or Ba, group IVb, such as Ti, Zr or Hf, group IIb such as Zn, Cd or Hg and group IVa such as Ge, Sn or Pb, said catalyst also comprising at least one matrix and, optionally at least one element selected from the group formed by IB and VIII of the periodic classification of the elements, for the dismutation of alkylaromatic hydrocarbons, preferably for the dismutation of toluene to produce benzene and xylenes, and/or for the transalkylation of alkylaromatic hydrocarbons, preferably for the transalkylation of toluene and trimethylbenzenes to produce xylenes.