Abstract: This invention relates to a method for reducing the content of sulfide-type compounds of formula R1-S—R2, with R1 and R2 selected from among the methyl (CH3) and ethyl (C2H5) radicals, of a gasoline that contains diolefins, monoolefins, and sulfur. The method implements a first catalytic step for selective hydrogenation of diolefins at a temperature of between 60° C. and 150° C. and then a step for heating the effluent that is obtained from the first step with a temperature difference ?T of between 10° C. and 100° C. and a second catalytic step on the effluent that is heated in such a way as to produce an effluent that has a content of sulfide-type compounds of formula R1-S—R2, with R1 and R2 selected from among the methyl (CH3) and ethyl (C2H5) radicals, lower than that of the starting gasoline.