A polyalkenyl succinic anhydride is prepared with low amounts of resinous or chlorinated byproducts in a two-step process whereby a polyalkene is first reacted with an unsaturated organic acid in a thermal ene reaction, followed with exposure to a gaseous halogen in presence of an additional amount of the unsaturated organic acidic reagent. The foregoing process produces a polyisobutenyl succinic anhydride having a high ratio of succinic anhydride functional groups to polyisobutenyl backbone groups. Such a polyisobutenyl succinic anhydride is particular suitable for the production of oil-soluble hydrocarbyl succinimides that have good dispersant properties when added to lubricating oil compositions.