The invention relates to a process for dyeing and/or lightening keratin materials, in particular keratin fibres, preferably human keratin fibres such as the hair, using at least one fluorescent direct dye bearing a disulfide, thiol or protected-thiol function and comprising at least one aliphatic chain of formula (I): A – (X)p – Csat – S – U. The invention also relates to the use i) of at least one fluorescent direct dye bearing a disulfide, thiol or protected-thiol function (I) combined with ii) steam and/or a heating iron for straightening keratin fibres, for dyeing and lightening keratin materials, and to novel fluorescent direct dyes bearing a disulfide, thiol or protected-thiol function of formula (I): A – (X)p – Csat – S – U, and also a cosmetic composition comprising same. The process used and the use of the thiol, protected-thiol or disulfide fluorescent direct dyes of formula (I) combined with steam makes it possible especially to obtain long-lasting colouring with care valency on keratin materials.
