Abstract: A process for the selective hydrodesulfurization of a naphtha containing olefins and organosulfur compounds is disclosed, which minimizes the hydrogenation of the olefins and results in a product with a low sulfur content. The process involves a two-stage hydrodesulfurization with H2S removed from the first stage effluent. A flow of hydrogen and at least one added non-reactive compound is fed into the first stage, wherein the H2 molar fraction ranges from 0.2 to 1.0, and with H2S at the reactor intake limited to a maximum of 0.1% by volume. The second stage involves a feedstream of hydrogen and at least one added non-reactive compound, wherein the H2 molar fraction ranges from 0.2 to 0.7 and with H2S at the reactor intake limited to a maximum of 0.05% by volume.