Composition containing, in a cosmetically or dermatologically acceptable medium, a compound that may be obtained by reaction between:an oil bearing at least one nucleophilic and/or electrophilic reactive function, anda junction group capable of establishing hydrogen bonds with one or more partner junction groups, the junction group bearing at least one reactive function capable of reacting with the reactive function borne by the oil, and also comprising at least one unit of formula (I) or (II):
