The present invention is relating to a cosmetic composition comprising: at least 2% by weight, with respect to the weight of the composition, of alkylcellulose, the alkyl residue of which comprises between 2 and 6 carbon atoms, preferably between 2 and 3, at least one non-volatile polar hydrocarbon first oil, at least 20% by weight, with respect to the weight of the composition, of at least one second oil, incompatible with the first oil or oils, chosen from non-volatile silicone oils, from non-volatile fluorinated oils, or their combinations, optionally at least one non-volatile third oil, different from the first oil or oils, chosen from polar or non-polar hydrocarbon oils, silicone oils different from the second oil or oils, phenylated oils not comprising a dimethicone fragment, or their mixtures, less than 5% by weight of water, with respect to the weight of the composition. The composition can comprise at least one wax.
The invention also relates to a method for making up and/or caring, in particular for the lips, in which the abovementioned composition is applied.