The invention describes polyisobutenyl derivatives of succinic acid obtainable by: i) reacting a polyisobutene which has a reactive end group content of at least 80% and whose molecular weight distribution is characterized by a maximum M.sub.P in the distribution curve in the range from 500 to 20 000 daltons and a ratio of weight average molecular weight to number average molecular weight M.sub.W/M.sub.N of below 1.4 with maleic acid or maleic anhydride; ii) reacting the polyisobutene-succinic acid derivative obtained in i) with at least one compound I which has at least one primary or secondary amino group and/or an OH group to form an amide or ester bond, and also a process for preparing them and their use as additives in lubricant compositions.