The invention relates to a process for the production of phenylalkanes comprising an alkylation reaction of at least one aromatic compound by at least one linear olefin having from 9 to 16 carbon atoms per molecule. Said reaction is carried out in a catalytic reactor in which n reaction zones are present each containing at least one same solid acid catalyst, n being greater than or equal to 2, and at the inlet to each of which at least one fraction of the total quantity of olefins necessary for said reaction is introduced. The phenylalkanes obtained by the process according to the invention are particularly suitable for manufacturing detergents.