A subject of the present invention is therefore a composition comprising, in a cosmetically acceptable medium: a) an aqueous phase and b) at least hydrophobic silica aerogel particles and; c) at least one alcohol of formula (I) below and also optical isomers thereof: R1 represents an —OH or CH2OH group; R2 represents a hydrogen atom or an —OH group; R3 represents a hydrogen atom or a linear or branched, saturated or unsaturated C1-C22 alkyl group; R4 represents a hydrogen atom, an —OH group, a —CH2OH group, a —CH(OH)—CH3 group, a —C(CH3)2—OH group, a —(O)—CH2—CH2)n—OH group, a —(O—CH2—CH(CH3))m—OH group or a —(CH2—CH2)p—OH group; n denotes an integer ranging from 1 to 10; m denotes an integer ranging from 1 to 10; p denotes an integer ranging from 1 to 5; with the proviso that at least one of the radicals R1, R2, R3 and R4 comprises at least one hydroxyl function; R5 represents a hydrogen atom or a linear or branched, saturated or unsaturated C1-C22 alkyl group and d) at least one deodorant active agent other than said alcohol of formula (I) and/or at least one antiperspirant active agent; said hydrophobic silica aerogel particles being dispersed in the aqueous phase. The present invention relates to a cosmetic treatment process for a keratin material for treating body odors associated with human perspiration, in particular underarm odors and optionally for treating human perspiration, which consists in applying, to the surface of said keratin material to be treated, at least one composition as defined above.