A hair colouring and/or bleaching composition obtained by mixing, prior to application onto hair, at least a first aqueous component (i) and a second aqueous component (ii), wherein: - the first aqueous component (i) comprises, in a cosmetically acceptable carrier: - one or more oxidizing agent(s) and - the second aqueous component (ii) comprises, in a cosmetically acceptable carrier: - one or more alkalizing agent(s) selected from the group consisting of ammonia, its salts and mixtures thereof, - and optionally one or more oxidative dyes or one or more direct dyes or a mixture of one or more oxidative dyes and one or more direct dyes wherein the first component (i) or the second component (ii) or both comprise at least a first and a second malodor suppressant and optionally one or more further malodor suppressants, or the first component (i) comprises at least a first malodor suppressant and the second component (ii) comprises at least a second malodor suppressant, the first and the second malodor suppressant and any further malodor suppressant forming a malodor suppressant system in the hair colouring and/or bleaching composition, and each of the first and second malodor suppressants being a compound having a distribution coefficient logP (octanol/water) of 2 or more and a molecular weight of between 100 and 400; wherein the first malodor and second malodor suppressant are isopropylmyristate and galaxolide, or isopropylmyristate and habanolide; wherein the first malodor suppressant or the combination of the first and second malodor suppressants is present in the first composition (i) and/or in the second composition (ii) in an amount of 0 to 70% by weight, and the combined amount of malodor suppressant in the first and second composition is at least 0.1% by weight. - the first aqueous component (i) comprises, in a cosmetically acceptable carrier: - one or more oxidizing agent(s) and - one or more oxidizing agent(s) and - the second aqueous component (ii) comprises, in a cosmetically acceptable carrier: - one or more alkalizing agent(s) selected from the group consisting of ammonia, its salts and mixtures thereof, - and optionally one or more oxidative dyes or one or more direct dyes or a mixture of one or more oxidative dyes and one or more direct dyes - one or more alkalizing agent(s) selected from the group consisting of ammonia, its salts and mixtures thereof, - and optionally one or more oxidative dyes or one or more direct dyes or a mixture of one or more oxidative dyes and one or more direct dyes wherein the first component (i) or the second component (ii) or both comprise at least a first and a second malodor suppressant and optionally one or more further malodor suppressants, or the first component (i) comprises at least a first malodor suppressant and the second component (ii) comprises at least a second malodor suppressant, the first and the second malodor suppressant and any further malodor suppressant forming a malodor suppressant system in the hair colouring and/or bleaching composition, and each of the first and second malodor suppressants being a compound having a distribution coefficient logP (octanol/water) of 2 or more and a molecular weight of between 100 and 400; wherein the first malodor and second malodor suppressant are isopropylmyristate and galaxolide, or isopropylmyristate and habanolide; wherein the first malodor suppressant or the combination of the first and second malodor suppressants is present in the first composition (i) and/or in the second composition (ii) in an amount of 0 to 70% by weight, and the combined amount of malodor suppressant in the first and second composition is at least 0.1% by weight.