The present invention relates to a care, and/or treatment, and/or make-up cosmetic composition for keratin materials, comprising, in a physiologically acceptable medium, an efficient amount of at least one linear, branched or cyclic polymer, or dendrimer, comprising: a -POL- polymeric backbone comprising at least two repeating patterns, and at least two binding groups (A), attached on the polymeric backbone and adapted to create H links with one ore more partner binding groups, of an identical or different chemical nature, each coupling of two binding groups involving at least three H links.