The invention relates to a cosmetic composition comprising, in a physiologically acceptable aqueous medium, a cucurbic acid compound of formula (I) in which R1 represents a radical COOR3, where R3 denotes H or a C1-C4 alkyl radical, which is optionally substituted by one or more hydroxyl groups; R2 represents a hydrocarbon radical having from 1 to 18 carbon atoms; and a copolymer of 2-acrylamido-2-methylpropanesulphonic acid and hydroxylated C2-C4 alkyl(meth)acrylate. Application to the care and make-up of keratin materials.