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The stability of an evaporating thin liquid film on a solid substrate is investigated within lubrication theory. The heat flux due to evaporation induces thermal gradients; the generated Marangoni stresses are accounted for. Assuming the gas phase at rest, the dynamics of the vapour reduces to diffusion. The boundary condition at the interface couples transfer from the liquid to its vapour and diffusion flux. The evolution of the film is governed by a lubrication equation coupled with the Laplace problem associated with quasi-static diffusion. The linear stability of a flat film is studied in this general framework. The subsequent analysis is restricted to diffusion-limited evaporation for which the gas phase is saturated in vapour in the vicinity of the interface. The stability depends then only on two control parameters, the capillary and Marangoni numbers. The Marangoni effect is destabilizing whereas capillarity and evaporation …