The present disclosure relates to anhydrous cosmetic compositions which contain a combination of a strongly swelling and a low-swelling water-absorbing component in combination with a deodorant active ingredient. These compositions have an outstanding deodorizing effect and improved sensory features and additionally result in a minimization of sweat spots on textiles. Furthermore, the present disclosure relates to a cosmetic product containing these anhydrous compositions and the use of the composition or product for reduction of the body odor released by perspiration. Finally, the present disclosure relates to the use a strongly swelling water-absorbing component to improve the sensory characteristics of anhydrous deodorant compositions.