Reaction products of polyolefins having predominantly a terminal double bond and a number average molecular weight of from 250 to 10,000, which possess an aliphatic hydrocarbon skeleton which is straight-chain or carries C.sub.1 -C.sub.4 -alkyl side chains, with from 1 to 10 mol, per equivalent of double bond, of one or more vinyl esters I ##STR1## are obtainable by reacting the stated polyolefins with the vinyl esters I in the presence of a free radical initiator at from 80 to 200.degree. C., it being possible for these reaction products subsequently to have been hydrolyzed to the corresponding alcohols or converted into the corresponding amines by reductive amination with amines II ##STR2## .