We study the evaporation of a droplet in its own stagnant vapor. Using three successive. asymptotic expansions we can deduce an analytic expression for the drop radius. The nondimensionalized numbers involved in the expansion are the Mach number, the ratio of the thermal diffusivities End the Stefan number. The results obtained improve the previous ones derived with the so called quasi-permanent hypothesis. The comparison with numerical computation shows that the expression obtained by singular perturbation is a good approximation.