Abstract: A process is described for producing additives for diesel fuels having high cetane numbers and serving as fuel ignition improvers. In the process, biomass feedstock selected from (a) tall oil containing less than 0.5 wt % ash, less than 25 wt % unsaponifiables, up to 50 wt % diterpenic acids and 30 to 60 wt % unsaturated fatty acids, (b) wood oils from the pulping of hardwood species, (c) animal fats and (d) blends of said tall oil with plant or vegetable oil containing substantial amounts of unsaturated fatty acids or animal fats, is subjected to hydroprocessing by contacting the feedstock with gaseous hydrogen under hydroprocessing conditions in the presence of a hydroprocessing catalyst to obtain a product mixture. This product mixture is then separated and fractionated to obtain a hydrocarbon product boiling in the diesel fuel boiling range, this product being the high cetane number additive.