Device having two or more compartments, or "kit", for dyeing keratin fibres, and in particular human keratin fibres such as the hair, in which a first compartment contains a dye composition free of oxidizing agent, comprising, in a suitable dyeing medium: - one or more hair dyes; - one or more fatty substances free of carboxylic acid groups, the amount of fatty substance in the dye composition being between 10% and 75% by weight; and - one or more polycondensates of ethylene oxide and propylene oxide consisting of polyethylene glycol and polypropylene glycol blocks having the following chemical structure: H-(O-CH 2 -CH 2 ) a -(O-CH(CH 3 )-CH 2 ) b -(O-CH 2 -CH 2 ) a' -OH in which formula a and a' range from 10 to 130 and b ranges from 20 to 80; with the exception of the following composition: INCI name g% Beheneth-10 6.00 Sorbitol 5.00 Liquid petroleum jelly 60.25 Water 10.00 Ethanol 2.00 Poloxamer 184 5.00 Potassium bicarbonate 1.75 Water 4.302 Monoethanolamine 5.00 p-Phenylenediamine 0.216 2,4-Diaminophenoxyethanol dihydrochloride 0.482 and of the following composition obtained by mixing the emulsion A1: Emulsion A1 Phase INCI name g% A Beheneth-10 6.00 Sorbitol 5.00 Liquid petroleum jelly 60.25 Water 10.00 B Ethanol 2.00 Poloxamer 184 5.00 Potassium bicarbonate 1.75 Water 4.302 Monoethanolamine 5.00 p-Phenylenediamine 0.216 2,4-Diaminophenoxyethanol dihydrochloride 0.482 with an aqueous composition (B) comprising a dispersion of fatty alcohols in water (8%) and 6% hydrogen peroxide in a ratio of 1 part by weight of (A1) per 1.5 parts by weight of (B); and a second compartment contains an oxidizing composition comprising one or more oxidizing agents chosen from hydrogen peroxide, urea peroxide, alkali metal bromates or ferricyanides, peroxygenated salts and alkali metal or alkaline-earth metal percarbonates for instance persulfates and perborates, peracids and precursors thereof, and percarbonates of alkali metals or alkaline-earth metals such as sodium, potassium or magnesium. - one or more hair dyes; - one or more fatty substances free of carboxylic acid groups, the amount of fatty substance in the dye composition being between 10% and 75% by weight; and - one or more polycondensates of ethylene oxide and propylene oxide consisting of polyethylene glycol and polypropylene glycol blocks having the following chemical structure: H-(O-CH 2 -CH 2 ) a -(O-CH(CH 3 )-CH 2 ) b -(O-CH 2 -CH 2 ) a' -OH in which formula a and a' range from 10 to 130 and b ranges from 20 to 80; with the exception of the following composition: INCI name g% Beheneth-10 6.00 Sorbitol 5.00 Liquid petroleum jelly 60.25 Water 10.00 Ethanol 2.00 Poloxamer 184 5.00 Potassium bicarbonate 1.75 Water 4.302 Monoethanolamine 5.00 p-Phenylenediamine 0.216 2,4-Diaminophenoxyethanol dihydrochloride 0.482 and of the following composition obtained by mixing the emulsion A1: Emulsion A1 Phase INCI name g% A Beheneth-10 6.00 Sorbitol 5.00 Liquid petroleum jelly 60.25 Water 10.00 B Ethanol 2.00 Poloxamer 184 5.00 Potassium bicarbonate 1.75 Water 4.302 Monoethanolamine 5.00 p-Phenylenediamine 0.216 2,4-Diaminophenoxyethanol dihydrochloride 0.482 with an aqueous composition (B) comprising a dispersion of fatty alcohols in water (8%) and 6% hydrogen peroxide in a ratio of 1 part by weight of (A1) per 1.5 parts by weight of (B); and a second compartment contains an oxidizing composition comprising one or more oxidizing agents chosen from hydrogen peroxide, urea peroxide, alkali metal bromates or ferricyanides, peroxygenated salts and alkali metal or alkaline-earth metal percarbonates for instance persulfates and perborates, peracids and precursors thereof, and percarbonates of alkali metals or alkaline-earth metals such as sodium, potassium or magnesium. <EOS>