In this study we perform a linear analysis of the stability of a two-layered liquid him which is evaporating upon a horizontal solid substrate. The film contains surfactant that is soluble in both liquid phases. The problem was solved in general form, in our previous work [cf. Danov et al. (1997b) Chem. Engng Sci., submitted] by using lubrication approximation. The governing equations for the film thickness and the surfactant concentration derived there are treated using linear analysis in the present study. The resulting system of ordinary differential equations describes the evolution of small long-wave disturbances of the film shape and the surfactant distribution during the film evaporation. The model allows one to investigate the role of different factors on the film stability. To illustrate the effects we consider a particular system : water-hexane him evaporating on a PVC plate. The limiting cases of pure liquids and tangentially immobile surfaces, as well as the general case are studied numerically. Both cases when a low- and a high-molecular weight surfactants present into the film are investigated. The numerical results in the case of non-linear stability analysis of a PVC/tetrachlorethane/water/vapour evaporating film are subject of part III [cf. Paunov et al. (1997) Chem. Engng Sci., submitted].