A problem of laminar film condensation from steam-gas mixtures between two coaxial cylinders is numerically analysed. A set of complete boundary layer equations is used to model simultaneous momentum, heat and mass transfer in the liquid film and the vapour-gas mixture. In order to locate accurately the liquid-mixture interface, a relevant change of coordinates is performed. Equations are solved using an implicit finite difference scheme. The liquid film thickness is determined from an iterative procedure based on the secant method. An analytical solution of the momentum equations of both phases at the end of condensation is also developed. Results presented include evolutions of field profiles and flow parameters from the inlet until the end of condensation. We also analyse the effects of the wall properties, the inlet conditions, the type of non-condensable gas, the size of the annular space and the convective cooling coefficient.