The present invention relates to a linear ethylenic block copolymer comprising in each block at least one ionic hydrophilic unit, which may be different from one block to another, the said ionic hydrophilic unit being present in each block in a proportion of from 2% to 100% by weight relative to the weight of the said block.The invention also relates to a cosmetic or pharmaceutical composition comprising such a copolymer, and also to a cosmetic process for making up or caring for keratin materials using the said composition.