The invention relates to a process of alkylating aromatic hydrocarbons, and more particularly a process of making paraxylene by alkylation of benzene and/or toluene with methanol and/or dimethyl ether, and to an apparatus for carrying out said process, the improvement comprising staged injection of one of the reactants, with the stages separated by structured packing so as to minimize at least one of gas phase back-mixing, by-pass phenomena, and gas bubble size.