To provide polyisobutenyl succinic anhydride especially suitable to produce oil-soluble hydrocarbyl succinimide that exhibits excellent dispersion characteristics when added to a lubricant composition.

Polyalkenyl succinic anhydride is prepared along with a small amount of resinous by-products or chlorinated by-products by a 2-stage process where a polyalkene is subjected to thermal ene reaction with an unsaturated organic acid and then to exposure to a halogen gas in the presence of the unsaturated organic acidic agent that is further added. The polyisobutenyl succinic anhydride having a high ratio of a succinic anhydride functional group to a polyisobutenyl skeleton group can be produced by this process.