Disclosed are hair care and hair cleansing compositions as well as skin care and skin cleansing compositions comprising a fibrous material of natural origin and obtained from plants. The fibrous material comprises micro-scaled and/or nano-scaled fibril agglomerates. Such compositions show pleasant skin feel and comfort during and after application, as well as fast drying and fast absorption into skin. The compositions obtained are also particularly well suited for the topical delivery of cosmetic and pharmaceutical active substances into skin. Additionally, a method to obtain said hair care or hair cleansing composition or said skin care or skin cleansing composition is disclosed.