A process for the production of phenyl alkanes by catalytic alkylation on a solid acid catalyst employs at least one moving-bed reactor. This process comprises a catalytic alkylation stage of an aromatic compound by at least one olefin that has 9 to 16 carbon atoms per molecule, combined with a catalyst reactivation circuit. Each reactor contains n reaction zones, whereby each of said zones consists of an acidic solid catalyst, optionally different from one zone to the next. Entering each reaction zone, a fraction of the total amount of olefins necessary to the alkylation reaction is introduced. The phenyl alkanes that are obtained by the process according to the invention are particularly suitable for the production of detergents.