A cosmetic product for the oxidative colour changing of keratin fibres, in particular human hair, comprises a preparation (A), which is packaged in a sachet (S), where- preparation (A) contains: (A1) water and (A2) hydrogen peroxide and (A3) at least one stabilizer from the group comprising 2,6-dipicolinic acid, 1-hydroxyethane1,1-diphosphonic acid (HEDP), benzoic acid, salicylic acid, ethylenediamine, tetra(methylenephosphonic acid) (EDTMP),diethylenetriamine penta(methylenephosphonic acid) (DTPMP), amino tris(methylenephosphonic acid) (ATMP), N,N-bis[2-[bis(carboxymethyl)amino]ethyliglycine, ethylenediamine-N,N'- disuccinic acid (EDDS), 2-hydroxypropylenediamine-N,N'-disuccinic acid (HPDDS),ethylenediamine-N,N'-diglutaric acid (EDDG), ethylenediamine-N,N'-bis(orthohydroxyphenyl)acetic acid (EDDHA), diphosphoric acid, hydrated tin oxide, and/or the physiologically acceptable salts thereof; and - the wall of sachet (S) comprises (S1) a first layer made of a first polymeric material and ( S2) a second layer made of a second polymeric material and (SBa) a barrier layer, which has a penetration barrier effect for gases and water vapour. The hydrogen peroxide may be present in the range of 1.5 to 12.0% by weight, preferably 9.0 to 12.0; and the one or more stabilizers may be present in the range 0.05 to 0.5% by weight, preferably 0.35 to 1.0% by weight. The barrier layer may comprise one or more inorganic/organic hybrid polymers.