The present invention relates to a cosmetic composition for dyeing keratin fibres, in particular human keratin fibres such as the hair, comprising, in a suitable dyeing medium, at least one hydroxyalkyl compound of general formula (I) below: ##STR00001## and at least one cosmetic adjuvant according to the invention. The present invention also relates to a process for dyeing keratin fibres using these compositions based on hydroxyalkyl compounds, to a device with compartments and to the use of these compounds in hair dyeing.