The present invention relates to a dye composition comprising: * at least one oxidation dye precursor; * at least one polycondensate of ethylene oxide and of propylene oxide having the structure (A) below H—(O—CH2—CH2)n—(O—CH(CH3)—CH2)b—(O—CH2—CH2)a—OH (A) in which formula a and a′ range from 2 to 150 and b ranges from 1 to 100; and * at least one C8-C30 fatty alcohol comprising at least one unsaturation. The invention also relates to a dyeing process using this composition (free of oxidizing agent) after mixing with a composition comprising an oxidizing agent. Another subject of the invention is a two-compartment device, the first compartment comprising the composition according to the invention, free of oxidizing agent, and the second compartment containing a composition comprising at least one oxidizing agent.