Process for the production of at least one compound that is selected from among monoalkyl aromatic compounds, dialkyl aromatic compounds and trialkyl aromatic compounds by alkylation or transalkylation of an aromatic compound by at least one alkylating agent that is selected from among the olefins, whereby the process is characterized in that it is carried out in one or two stages, involving two reaction zones in series, whereby one of these two zones can be switched off so as to be able, depending on whether or not one of the zones is switched off, to meet the demand either of the three types of mono, di- and trialkyl aromatic compounds, or two of these types or a single one of the types of mono- or di- or trialkyl aromatic compounds.