  An useful approximation for the displacement of two immiscible fluids in a
porous medium is the Hele-Shaw model. We consider several liquids with
different constant viscosities, inserted between the displacing fluids. The
linear stability analysis of this model leads us to an ill-posed problem. The
growth rates (in time) of the perturbations exist iff some compatibility
conditions on the interfaces are verified. We prove that these conditions
cannot be fulfilled.
