The invention relates to a process for the production of at least one compound that is selected from among the 2-, 3-, 4-, 5-, and 6-phenylalkanes by alkylation of an aromatic compound by means of at least one olefin that comprises at least 9 carbon atoms per molecule, in the presence of a catalyst that comprises at least one non-zeolitic substrate with a silicated alumina base that contains an amount of more than 6% by weight and less than or equal to 50% by weight of silica (SiO2) and that exhibits particular characteristics, whereby said process is carried out at a temperature of between 30 and 400.degree. C., a pressure of between 0.1 and 10 MPa, an hourly volumetric flow rate of 0.50 to 200 h-1, and an aromatic compound/olefin molar ratio of between 1:1 and 50:1.