  In this paper we consider a two-phase thin film consisting of two immiscible
viscous fluids endowed with a layer of insoluble surfactant on the surface of
the upper fluid. The governing equations for the two film heights and the
surfactant concentration are derived using a lubrication approximation. Taking
gravitational forces into account but neglecting capillary effects, the
resulting system of evolution equations is parabolic, strongly coupled, of
second order and degenerated in the equations for the two film heights.
Incorporating on the contrary capillary forces and neglecting the effects of
gravitation, the system of evolution equations is parabolic, degenerated and of
fourth order for the film heights, strongly coupled to a second order transport
equation for the surfactant concentration. Local well-posedness and asymptotic
stability are shown for both systems.
