A cosmetic composition includes, in a physiologically acceptable medium: at least water, at least alkylcellulose, at least one first hydrocarbon-based non-volatile oil, chosen from: C10-C26 alcohols, preferably monoalcohols; optionally hydroxylated monoesters, diesters or triesters of a C2-C8 monocarboxylic or polycarboxylic acid and of a C2-C8 alcohol; esters of a C2-C8 polyol and of one or more C2-C8 carboxylic acids. At least one second non-volatile oil chosen from silicone oils and/or fluoro oils or hydrocarbon-based oils other than the said first oil; at least one stabilizer chosen from surfactants and/or hydrophilic gelling agents, preferably chosen from associative polymers, natural polymers and their mixture.