A process for preparing oligomers and polymers, obtained from A) from 0.001 to 100 mol % of at least one aminoalkene of the formula I ##STR1## where X is an integer from 0 to 25 and R.sup.1 to R.sup.6 are hydrogen, C.sub.1 - to C.sub.10 -alkyl, 5- to 7-membered cycloalkyl which, in turn, can carry C.sub.1 - to C.sub.6 -alkyl groups as substituents or C.sub.6 - to C.sub.15 -aryl and B) from 0 to 99.999 mol % of at least one alkene, for x=1 in formula I propene being excluded as component B).