The present disclosure relates to an antiperspirant cosmetic agent containing:a) from about 0.5 to about 7.0% by weight of at least one copolymer formed from the monomers i) N-tert-octylacrylamideii) acrylic acidiii) tert.-butylaminoethyl methacrylateiv) and optionally further monomersb) from about 40 to about 75% by weight of oil that is liquid at about 20° C. and about 1.013 hPa wherein the antiperspirant cosmetic agent does not contain any aluminium-containing compounds, use thereof, and methods using an agent of this kind.