Production of gasolines with low sulfur contents from a starting gasoline containing sulfur-containing compounds comprising a stage a) for selective hydrogenation of non-aromatic polyunsaturated compounds present in the starting gasoline, a stage b) for increasing the molecular weight of the light sulfur-containing products that are initially present in the gasoline that enters this stage, a stage c) for alkylation of at least a portion of the sulfur-containing compounds present in the product that originates from stage b), a stage d) for fractionation of the gasoline that originates from stage c) into at least two fractions, one fraction virtually lacking in sulfur-containing compounds, whereby the other contains a larger proportion of sulfur-containing compounds (heavy gasoline), a stage e) for catalytic treatment of the heavy gasoline for transformation of sulfur-containing compounds under conditions for the at least partial decomposition of hydrogenation of these sulfur-containing compounds.