Disclosed herein is a device having one or more compartments, for dyeing keratin fibers, wherein 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, and optionally a second compartment contains an oxidizing composition. Also disclosed is an agent for dyeing and/or bleaching keratin fibers, 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, with a weighted HLB of greater than or equal to 8, the amount of fatty substance being greater than 20% of the total weight of the dyeing and/or bleaching agent.