The benzene content of hydrocarbon gasolines is accomplished by (a) fractionating at least one hydrocarbon gasoline into a light fraction A, with an increased benzene content, and a heavy fraction B, with a reduced benzene content; (b) contacting the light fraction A at a temperature below room temperature with a gas containing at least a fraction of olefins in which the number of carbon atoms is from 2 to 5 per molecule so that at least a fraction of said olefins is absorbed in light fraction A; at the end of stage (b), separating a residual gas with a reduced olefin content from a liquid fraction C, with an increased olefin content; (d) passing the fraction C from stage (c) into an alkylation reactor so that at least a fraction of the benzene is alkylated by at least a fraction of the olefins; (e) fractionating the mixture emerging from stage (d) so as to produce, firstly, a gas phase chiefly comprising gases which were not converted during stage (d) and, secondly, a liquid phase, at least partly containing the non-alkylated benzene and alkylbenzenes; and (f) mixing the liquid phase from stage (e) with the heavy fraction B from stage (a).