A process for hydrodesulphurizing gasoline cuts is carried out in the presence of a catalyst comprising at least one group VIII element, at least one group VIB element, and a support with a specific surface area of less than about 200 m.sup.2/g, wherein the density of the group VIB elements per unit surface area of the support is in the range 4.times.10.sup.-4 to 36.times.10.sup.-4 g of group VIB element oxides per m.sup.2 of the support.