The invention relates to a device having one or more compartments, or “kit”, for dyeing keratin fibres, in which a first compartment contains a dye composition free of oxidizing agent, comprising at least one hair dye and at least one polycondensate of ethylene oxide and propylene oxide consisting of polyethylene glycol and polypropylene glycol blocks, and optionally a second compartment contains an oxidizing composition.The invention also relates to an agent for dyeing and/or bleaching keratin fibres, obtained by mixing a composition A comprising at least one alkaline agent with a composition B comprising at least one oxidizing agent, compositions A and/or B comprising at least one fatty substance free of carboxylic acid groups, at least one polycondensate of ethylene oxide and propylene oxide, and a system of nonionic surfactants other than polycondensates of ethylene oxide and propylene oxide, with a weighted HLB of greater than or equal to 8, the amount of fatty substance being greater than 20% by weight relative to the total weight of the dyeing and/or bleaching agent.