The aim of this study is to perform a stability analysis of a thermo-capillary flow in a steady-state evaporating/condensing liquid layer applying the statistical rate theory expression for the mass flux across the interface. In the general mass, momentum and energy balance equations, the effects of gravity, temperature gradients in the surface tension, the interfacial momentum and energy loss due to the net mass flux are taken into account. Assuming a non-deformable surface and low dynamic viscosity and thermal conductivity of the vapor, the stability problem of the liquid phase is separated from that for the vapor. The exact solution is found and the dispersion relationship is solved numerically for water. The numerical results show that the interfacial instability mode always takes place in spite of the direction of the mass flux across the interface. The main physical reason for this kind of instability is the strong dependence of the mass flux on the vapor pressure predicted from the statistical rate theory. Other internal instability modes are described as a function of the Rayleigh and Marangoni numbers. The stability diagrams are discussed in the light of the available experiments for controllable water steady-state evaporation and condensation.