For the production of gasoline with a low sulfur content, a process comprises at least one stage for transformation of sulfur-containing compounds consisting of an alkylation or adsorption of sulfur-containing compounds and/or an increasing of the weight of light sulfur-containing compounds, at least one stage for treatment in the presence of an acid catalyst and at least one desulfurization treatment of at least a portion of the gasoline. The process can also optionally comprise at least one stage for selective hydrogenation of diolefins and optionally at least one fractionation of the gasoline that is obtained into at least two fractions: light gasoline and heavy gasoline.