The invention concerns the catalytic alkylation of at least one isoparaffin selected from the group formed by isobutane and isopentane in the presence of at least one olefin containing 3 to 6 carbon atoms per molecule, using a catalyst comprising 40% to 99% by weight of an acid selected from acids with formula R--SO.sub.3 H where R is fluorine or an alkyl group or a fluorinated alkyl group, R preferably being F or CF.sub.3, and more preferably CF.sub.3, and 1% to 60% by weight of a solvent selected from the group formed by sulpholane, dimethylsulphoxide and dioxanes, preferably sulpholane.