The present invention relates to a non-colouring composition comprising: one or more sulfureous reducing agents, the sulfureous reducing agent(s) being present in proportions ranging from 1.0% to 50.0% by weight relative to the total weight of the composition； one or more phosphoric surfactants； one or more nonionic surfactants other than the phosphoric surfactants； and at least 5.0% by weight of non-liquid fatty substance relative to the total weight of the composition. The invention also relates to a process for permanently reshaping keratin fibres using the composition.
