The invention relates to the use of a water-soluble or water-dispersible linear block copolymer comprising at least one hydrophulic block and at least one hydrophobic block, the hydrophilic block representing at least 30% by weight of the linear block copolymer, with the exclusion of block copolymers of ethylene oxide and propylene oxide, block copolymers containing urethane units and block copolymers containing siloxane units, to thicken or gel aqueous hair treatment compositions containing at least one polymer that is beneficial for the hair, and also to aqueous hair compositions thickened or gelled with such a block copolymer.