  In this paper we consider the evolution of two fluid phases in a porous
medium. The fluids are separated from each other and also the wetting phase
from air by interfaces which evolve in time. We reduce the problem to an
abstract evolution equation. A generalised Rayleigh-Taylor condition
characterizes the parabolicity regime of the problem and allows us to establish
a general well-posedness result and to study stability properties of flat
steady-states. When considering surface tension effects at the interface
between the fluids and if the more dense fluid lies above, we find bifurcating
finger-shaped equilibria which are all unstable.
