A process for dyeing hair, by oxidation, in several stages, which comprises, in one of the stags, in applying to the hair a dyeing composition containing one or more oxidation dye precursors selected from the group consisting of a para-phenylenediamine, a para-aminophenol, 2,5-diaminopyridine, 2-hydroxy-5-aminopyridine, tetraaminopyrimidine, 1-amino-2-hydroxybenzene, 6-methyl-1-hydroxy-2-aminobenzene, 4-methyl-1-amino-2-hydroxybenzene, an ortho-phenylenediamine and a bisphenylenealkylenediamine of formula (III) and their addition salts with acids:
- ##STR12## in which:
- Z.sub.1 and Z.sub.2, which are identical or different, represent a hydroxyl or NHR.sub.9 groups, where R.sub.9 denotes a hydrogen atom or a lower alkyl radical;
- R.sub.6 and R.sub.7, which are identical or different, represent a hydrogen atom, a halogen atom or an alkyl group;
- R.sub.8 represents a hydrogen atom, an alkyl or hydroxyalkyl group, or an aminoalkyl group whose amino residue is unsubstituted or substituted by one or two alkyl groups;
- Y represents a radical selected from the group of radicals consisting of:
- ##STR13## in which n is an integer between 0 and 8 and m is an integer between 0 and 4, and in which the alkyl or alkoxy radicals indicated above denote a group having 1 to 4 carbon atoms or mixtures thereof, and then, in another stage, applying a dyeing composition containing, as coupler in an aqueous or dilute alcoholic vehicle, one or more hydroxybenzofurans of formula (I):
- ##STR14## or one of its salts in which R.sub.1 and R.sub.2, which are identical or different, represent a hydrogen atom or a C.sub.1 -C.sub.6 alkyl radical, R.sub.1 and R.sub.2 can occupy any position on the benzofuran ring provided that when R.sub.1 and R.sub.2 both denote an alkyl radical, they do not occupy the positions 2 and 3 at the same time, the concentration of the hydroxybenzofurans of formula (I) being 0.05 to 3.5% by weight of the total weight of the composition, an oxidizing agent being present in the composition applied in the second stage, or the oxidizing agent being applied to the hair itself in a third stage, allowing it to act for 10 to 40 minutes, and then rinsing the hair, washing it with shampoo, rinsing it again and drying it.