The present invention relates to a hair colouring and/or bleaching composition comprising at least a first aqueous component (i) and a second aqueous component (ii) being mixed prior to application onto hair, 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 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 log P of 2 or more and a molecular weight of between 100 and 400. The invention further relates to a hair colouring or bleaching kit comprising an individually packaged first and second aqueous component, a method of treating hair, a method of sequential oxidative hair colouring or hair bleaching and the use of at least a first and a second malodor suppressant as a malodor suppressant system in a composition for the treatment of hair.