The invention relates to a process for the production of a mixture of compounds that comprises for the most part at least one mono-alkylbenzene that belongs to the group that is formed by the 2-, 3-, 4-, 5- and 6-phenylalkanes by alkylation of benzene with at least one monoolefin that comprises at least two carbon atoms in its molecule, in the presence of a catalyst that comprises 12-tungstophosphoric acid and/or 12-tungstomolybdic acid, deposited on a substrate that develops a large specific surface area and a high pore volume and that comprises a majority proportion of zirconium oxide (ZrO.sub.2).