A process for the selective hydrodesulfurization of naphtha streams containing a substantial amount of olefins and organically bound sulfur. The naphtha stream is selectively hydrodesulfurized by passing it through a first reaction zone containing a bed of a first hydrodesulfurization catalyst, then passing the resulting product stream through a second reaction zone containing a bed of a second hydrodesulfurization catalyst, which second hydrodesulfurization catalyst contains a lower level of catalytic metals than the first hydrodesulfurization catalyst.