Process for desulfurization of an effluent for cracking or steam-cracking hydrocarbons, more particularly a gasoline for example for catalytic cracking that comprises the elimination of thiophenic compounds by alkylation of these compounds, followed by a distillation, a hydrocracking of said alkyl-thiophenic compounds, then a hydrodesulfurization of the effluent that is obtained from the hydrocracking zone. In a preferred embodiment, this process comprises a preliminary stage for separating the cracking or steam-cracking effluent into three fractions, and proposes sending to the alkylation stage only the intermediate fraction that is low in heavy basic nitrogen-containing compounds that are initially present in the effluents that are to be alkylated.