The present invention relates to a composition in the form of an oil-in-water emulsion comprising, in a cosmetically acceptable medium: a) a continuous aqueous phase and b) an oily phase dispersed in the said aqueous phase and c) at least one water-insoluble block film-forming ethylenic polymer, the said polymer comprising a first block with a glass transition temperature (Tg) of greater than or equal to 85°C and a second block with a Tg of less than or equal to 20°C and d) at least one aluminium and/or zirconium antiperspirant salt or complex.The present invention relates to a cosmetic treatment process for treating human perspiration and, where appropriate, the body odour associated with human perspiration, especially underarm odour, consisting in applying to the surface of the skin to be treated at least one composition as defined previously.
