The heat and mass transfer in a rarefied gas between its two parallel condensed phases is considered on the basis of linearized and non-linear S-model kinetic equations. The profiles of the macroscopic parameters in the gap between gas-liquid interfaces are obtained for several Knudsen numbers and for the cases of complete and non-complete evaporation and condensation. The linearized Navier-Stokes equations and energy equation, subjected to the temperature and pressure jump boundary conditions, are solved analytically and the expressions for the macroscopic parameters are obtained. The comparison of three approaches allowed us to establish the limit of the application of the linearized approaches in term of the saturation temperature ratio between the condensed phases. (C) 2018 Elsevier Ltd. All rights reserved.