The present invention is directed to an oil-soluble oleaginous composition additive comprising at least one terminally unsaturated ethylene alpha-olefin polymer of from above 20,000 to about 500,000 number average molecular weight substituted with mono- or dicarboxylic acid producing moieties (preferably dicarboxylic acid or anhydride moieties), wherein the terminal unsaturation comprises terminal ethenylidene unsaturation. The mono- and dicarboxylic acid or anhydride substituted polymers of this invention are useful per se as additives to oleaginous compositions such as lubricating oils, and can also be reacted with a nucleophilic reagent, such as amines, alcohols, amino alcohols and reactive metal compounds, to form products which are also useful oleaginous composition additives, e.g., as multifunctional viscosity index improvers.