The invention relates to water-free compositions, having: at least one oil, and a combination of thickeners, including: a) at least one silicone elastomer, b) at least one straight-chained or branched, saturated or unsaturated alcohol having more than 18 carbon atoms, and c) at least one clay mineral mixture modified with quaternary ammonium compounds. The water-free compositions are suitable in particular as soft solid preparations for use on the human skin. In particular, the compositions are suitable as a soft solid antiperspirant composition.