The present invention relates to a mascara composition including a cosmetically acceptable aqueous medium, characterized in that it includes an oily phase including at least one ethylene/vinyl acetate copolymer, and at least one wax or a mixture of waxes in a certain weight ratio. The present invention also relates to a process for the care or make-up of eyelashes or eyebrows, characterized by the fact that a composition according to the invention is applied to the eyelashes or eyebrows. It also relates to the use of a composition according to the invention in order to obtain a make-up for filling and/or curling the eyelashes and/or a smooth and uniform deposition on the eyelashes.