Process for preparing a macromonomer, in which a starting compound H2C═CR1—C6H4-s(R4)s—R3—OH or H2C═CR2—CO—NH—R3—OH, where R1 and R2 are each H or a linear or branched alkyl radical having from 1 to 4 carbon atoms, R3 is a linear or branched alkylene, aralkylene radical which has from 1 to 20 carbon atoms and can contain one or more hydroxy groups and the radicals R4 are each, independently of one another, a linear or branched alkyl, aralkyl, alkoxy or aralkoxy radical having from 1 to 20 carbon atoms and s=0-4, is, after partial deprotonation, reacted with at least one hydroxy-functional oxirane compound in the presence of an inhibitor of free-radical polymerization with opening of the oxirane ring, where the molar ratio of the molar amounts used n(starting compound):n(oxirane compound) is in the range from 1:100 to 1:1.Macromonomers which can be obtained by the process, polymers which can be obtained therefrom and their use as additives in coating compositions, plastics and cosmetics.