Composition containing, in an aqueous medium:from 0.1% to 20% by weight of one or more volatile linear alkanes,from 0.5% to 25% by weight of one or more silicones having a viscosity of greater than or equal to 20 000 mm2/s,one or more non-silicone fatty substances,in a weight ratio of non-silicone fatty substance(s)/silicone(s) having a viscosity of greater than or equal to 20 000 mm2/s of less than or equal to 5. Use thereof for the cosmetic treatment of keratin materials, preferably keratin fibers such as the hair.