Functionalized cyclopentene-derived oligomer mixtures are prepared by reacting oligomer mixtures which contain ethyleneic double bonds in one or more reaction steps starting from cyclopentene-derived oligomer mixtures of the formula I R.sup.1 R.sup.2 C.dbd.[.dbd.CH--(CH.sub.2).sub.3 --CH.dbd.].sub.n.dbd.CR.sup.3 R.sup.4 (I) where n is an integer from 1 to 15, and R.sup.1, R.sup.2, R.sup.3 and R.sup.4 are, independently of one another, hydrogen or alkyl, and are used as described.