Abstract: A process for the selective hydrodesulfurization of naphtha streams containing olefins and organosulfur compounds that minimizes olefin hydrogenation and results in a reduced sulfur content product. This is attained by two-stage hydrodesulfurization and H2S removal from the first stage effluent, with the first reaction stage catalyst being a more active HDS catalyst than the second reaction stage catalyst. Hydrogen and a non-reactive compound are fed to the first stage, with the H2 mole fraction in the mixture of H2 and non-reactive compound being from 0.2 to 1.0. H2S at the reactor inlet is limited to not more than 0.1% by volume. Hydrogen and a non-reactive compound are fed to the second reaction stage, the H2 mole fraction in the mixture of H2 and non-reactive compound being from 0.2 to 0.7. H2S at the reactor inlet is limited to not more than 0.05% by volume.