An improved oxidative process that employ a robust, non-aqueous, and oil-soluble organic peroxide oxidant for effective desulfurization and denitrogenation of hydrocarbons including petroleum fuels, hydrotreated vacuum gas oil (VGO), non-hydrotreated VGO, petroleum crude oil, synthetic crude oil from oil sand, and residual oil. Even at low concentrations and without the assistance of catalysts, the non-aqueous organic peroxide oxidant is extremely active and fast in oxidizing the sulfur and nitrogen compounds in the hydrocarbon feedstocks. Furthermore, the process generates a valuable organic acid by-product that is also used internally as the extractive solvent for effective removal of the oxidized sulfur and nitrogen from the hydrocarbons without the need of a final adsorption step. Novel process steps are also disclosed to substantially prevent yield loss in the oxidative process.