A multi-component packaging unit includes a first container containing a color changing preparation comprising, in a cosmetic carrier, a color-changing component and a second container packaged separately from the first container and containing an oxidizing agent preparation. The oxidizing agent preparation comprises at least two phases separated from one another. A first phase has an aqueous phase that comprises, in a cosmetically acceptable carrier, a chemical oxidizing agent and an anionic polymeric thickener chosen from homo- and copolymers of acrylic acid and methacrylic acid. A second phase has a hydrophobic phase that comprises an oil chosen from paraffin oil, liquid carboxylic acid esters of C2 to C8 monoalkanol with a mono- or dicarboxylic acid, and combinations thereof.