Deep desulfurization of hydrocarbon feeds containing undesired organosulfur and organonitrogen compounds to produce a hydrocarbon product having low levels of sulfur-containing and nitrogen-containing compounds, is achieved by first subjecting the entire feed to an extraction zone to separate an aromatic-rich fraction containing a substantial amount of the refractory organosulfur and organonitrogen compounds and an aromatic-lean fraction containing a substantial amount of the labile organosulfur and organonitrogen compounds. The aromatic-lean fraction is contacted with a hydrotreating catalyst in a hydrotreating reaction zone operating under mild conditions to convert the labile organosulfur and organonitrogen compounds. The aromatic-rich fraction is oxidized to convert the refractory organosulfur and organonitrogen compounds to oxidized organosulfur and organonitrogen compounds. These oxidized organosulfur and organonitrogen compounds are subsequently removed, producing a stream containing reduced levels of organosulfur and organonitrogen compounds.