The present invention relates to a composition comprising: (i) at least 20% by weight, relative to the total weight of the composition, of at least one C2-C4 monoalcohol; (ii) at least one polycondensate of ethylene oxide and of propylene oxide; and (iii) at least one nonionic surfactant other than the polycondensates (ii). The invention also relates to the use of this composition for cleansing the hair, and to a process for cleansing the hair using this composition.