The invention relates to a process for conversion of a gasoline-range hydrocarbon feed into a gasoline fraction with a higher octane rating than that of the feedstream, and a gasoil fraction with a cetane number higher than 45, including the following steps: a) a membrane separation step (B) applied to the hydrocarbon feed under conditions enabling selective separation of the majority of the linear olefins present in said feed and constituting the β fraction, the fraction containing the majority of the branched olefins, termed the γ fraction, constituting a gasoline with a high octane rating, greater than that of the feed, b) an oligomerisation step (C) applied to the linear olefins (β fraction) contained in the effluent stream from the membrane separation step (B) under moderate oligomerisation conditions, c) a distillation separation step (D) applied to the effluent stream arising from the oligomerisation step in at least two fractions, d) a hydrogenation step (E) applied to one of the fractions obtained at step c).