A dyeing composition for hair with improved dyeing and conditioning properties of hair, based on at least one oxidizing agent and at least one hair dye and comprising a polyhydroxy carboxylic acid as a chelating agent. The compositions of the present invention may be aqueous compositions. The preferred polyhydroxy carboxylic acid is gluconic acid and its salts. The oxidizing agent may be hydrogen peroxide. The hair dye may be an oxidation dye precursor and/or a direct dye. A kit for dyeing hair comprises one composition comprising a hair dye and a polyhydroxy carboxylic acid and another composition comprising an oxidizing agent. A process for dyeing hair comprises mixing a composition comprising a hair dye and a polyhydroxy carboxylic acid with an aqueous oxidizing composition, applying to hair and rinsing after 1 to 45 minutes.
