Subject of the paper are multicomponent phase equilibria between extremely thin liquid films and their vapour phase on curved or planar solid surfaces. The solid surface is either heated or cooled, so that the liquid films are evaporating or the vapour is condensing.The curvature of the film surface and long range molecular forces due to the van der Waals attraction acting over distances of about 0.2-100 nm between solid and liquid film can lead to a composition shift in liquid and vapour phase compared to the composition that would be observed at planar and not extremely thin liquid films in equilibrium with their vapour phase.The Kelvin equation for the interfacial pressure is derived, as well as the equations for the composition shift. As a numerical example shows the van der Waals forces considerably influence the pressures at the liquid-vapour interface. Responsible for the composition shift is a dimensionless thermodynamic quantity D-i = (1/RmTPh)(partial derivative(V) over bar /partial derivativex(i))'sigmaK. For small values D-i --> 0, liquid-vapour phase equilibria become identical with those of planar surfaces. For D-i > 0 the vapour phase contains less and for D-i < 0 more of the lighter volatiles than planar interfaces. (C) 2003 Elsevier Ltd. All rights reserved.