An asymptotic analysis is presented for the problem of droplet vaporization in a stagnant atmosphere taking into account the unsteady effects in the gas phase. The ratio of the densities of the ambient gas and of the liquid is considered as a small parameter. The results of the classical quasi-steady theories are recovered in the first approximation, and corrections due to unsteady effects are obtained for the vaporization rate and for the droplet lifetime, which are found to be of the order of the square root of the density ratio