The invention relates to an oily cosmetic composition comprising: - at least one sunflower wax, - at least one nonionic surfactant chosen from fatty acid esters of polyglycerol comprising from 2 to 9 glycerol units, fatty alkyl ethers of glycerol or of polyglycerol comprising from 1 to 9 glycerol groups, fatty acid esters of sucrose, oxyethylenated fatty acid esters comprising at least 8 oxyethylene groups, and caprylic acid esters of glycerol, and mixtures thereof, and - at least one oil. The composition may be used especially for removing makeup from the skin and/or the area around the eyes and/or from the lips.
