The present invention relates to a process for treating keratin fibers such as the hair using a packaging article comprising i) an envelope defining at least one cavity, the envelope comprising water-soluble and/or liposoluble fibres, preferably water-soluble fibres; ii) at least one anhydrous oxidizing composition, preferably in paste or powder form, comprising at least one anhydrous chemical oxidizing agent, preferably in paste or powder form; it being understood that the oxidizing composition is in one of the cavities defined by the envelope i).