A process is described for the hydrogenation of olefinic streams containing sulfurated compounds, obtained starting from hydrocarbon cuts containing isobutene (by means of selective dimerization), characterized by fractionating said streams in one or more distillation columns and hydrogenating separately the two fractions obtained. The stream at the head, with a minimum content of sulfurated compounds, is hydrogenated with conventional catalysts based on nickel or noble metals (Platinum and/or Palladium), extremely active but also very sensitive to sulfur, whereas the bottom of the column, rich in sulfurated compounds, is treated with bimetallic catalysts (for example Ni/Co and/or Ni/Mo), less active but not deactivated by sulfur.