Polyalkenylsuccinic acid derivatives are prepared by reacting oligo- or polyolefins having a number average molecular weight (M.sub.N) of from 500 to 10,000 with maleic acid derivatives I ##STR1## where R and R', independently of one another, are each hydroxyl, lower alkyl or halogen or together are oxygen, at elevated temperatures by a process in which effective amounts of free radical acceptors, such as oxygen, are present in the gas phase and in the liquid phase of the reacting system during the reaction. These polyalkenylsuccinic acid derivatives are suitable, after additional imidation, amidation or esterification, as fuel and lubricant additives.