The present invention relates to an anhydrous composition comprising, in a cosmetically acceptable medium: a) at least hydrophobic silica aerogel particles with a specific surface area per unit of mass (SM) ranging from 500 to 1500 m2/g, preferably from 600 to 1200 m2/g and better still from 600 to 800 m2/g, and a size expressed as the mean volume diameter (D[0.5]) ranging from 1 to 30 μm； b) at least one solid fatty substance； c) at least one oil； the said composition having a hardness measured at 32° C. and at a humidity of 40% ranging from 15 kPa to 150 kPa and preferably ranging from 20 kPa to 100 kPa. The present invention also relates to a cosmetic process for treating and/or caring for human keratin materials, characterized in that it consists in applying to the surface of the keratin material at least one composition as defined previously. The present invention also relates to a cosmetic process for treating human perspiration and/or perspiration-related body odour, which consists in applying to the surface of a human keratin material at least one composition as defined previously comprising at least one deodorant active agent and/or one antiperspirant active agent.
