The present invention concerns a cosmetic antiperspirant composition comprising at least one substance selected from the group consisting of cosmetic oils which are liquid at 20° C. and 1,013 hPa, odorants and waxes, at least one antiperspirant aluminum salt in a total amount of 1 to 80 wt %, based on the total weight of the cosmetic antiperspirant composition, and at least one compound of the formula (S-I), in which X+ is H+, Li+, Na+, K+, NH4+, ½ Mg2+, ½ Ca2+, ½ Mn2+, ½ Zn2+, ⅓ Al3+, ¼ Zr4+ or at least one antiperspirant aluminum salt and R1 is a linear or branched, saturated or unsaturated alkyl group having 1 to 10 carbon atoms, the addition of the at least one compound of the formula (S-I) resulting in effective activation of the at least one antiperspirant aluminum salt, in eminent stabilization of this activated state and in outstanding sweat diminution.