The invention relates to viscosifiers, especially terminated polymers that have functional terminal groups, said polymers being pre-extended by polyamines, polymercaptans, (poly)aminoalcohols, (poly)mercaptoalcohols or (poly)aminomercaptans and being reacted to give polymers that are terminated by other functional groups. The viscosifiers have a low content in educts or educt descendants that deteriorate the properties of compositions. They are also charaterized in that the formation of high-molecular addition products is considerably reduced or even excluded so that products obtained have low viscosity and good storage stability. The epoxy-terminated polymer of formula (I) is especially preferred.