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While the stability of liquid films on substrates is a classical topic of colloidal science, the availability of nanostructured materials, such as nanotubes, nanofibres and nanochannels, has raised the question of how the stability of liquid films and their wetting behaviour is affected by nanoscale confinement. This paper will present the conditions for the stability of liquid films on and inside cylindrical solid substrates with nanometre scale characteristic dimensions. It is shown that the stability is determined by an effective disjoining/conjoining pressure isotherm which differs from the corresponding disjoining/conjoining pressure isotherm of flat liquid films on flat solid substrates. From the former, the equilibrium contact angles of drops on an outer or inner surface of a cylindrical capillary have been calculated as a function of surface curvature, showing that the expressions for equilibrium contact angles vary for different geometries, in view of the difference in thickness of the film of uniform thickness with which the bulk liquid (drops or menisci) is at equilibrium. These calculations have been extended to the case of glass nanocapillaries and carbon nanotubes, finding good agreement with experimental results in the literature.