A new set of equations describing the growth and evaporation of stationary liquid droplets in a mixture of pure vapour and inert gas is presented. The equations, which model the heat and mass transfer between the droplet and its environment, are presented in a simple algebraic form and are suitable for practical calculations of droplet growth at any Knudsen number and at any concentration of inert gas. In particular, they are not restricted to the so-called quasi-steady regime of droplet growth when the droplet surface temperature has relaxed to its steady-state value. The physical model on which the theory is based is essentially that of Langmuir but some novel features are incorporated. Thus, the velocity distribution functions for vapour and inert gas molecules approaching the liquid surface are assumed to correspond to simplified Grad thirteen-moment distributions and this allows correct representation at a molecular level of the heat and mass fluxes at the outer edge of the Knudsen layer. In contrast to most simple models of condensation and evaporation, the theory predicts finite (as opposed to zero) temperature and vapour pressure jumps across the Knudsen layer in the continuum limit and shows that the former is directly proportional to the concentration of vapour present. The analysis also provides a physical interpretation for the origins of the reversed temperature gradient phenomenon in the Kundsen layer, an unusual feature predicted by more complex solutions of the Boltzmann equation itself. The transition from diffusion to kinetic control as the pure vapour limit is approached is also modelled by the theory which shows that the range of Knudsen numbers over which this occurs is of the same order as the mole fraction of inert gas present.