ABSTRACT The theory of stability of plane saturation fronts of permanent form in mathematical models of immiscible displacement that was presented in SPE 12691 is developed further. Stability of the saturation profile to normal modes of smal1-amplitude perturbations in pressures and saturation is found by solving the generalized eigenproblem to which linear stability analysis leads. Adaptive discretization into subdomains, simple finite element basis functions, and the Galerkin method are used to compute the growth or decay rate of incipient fingers of small and moderate width across the front. An expansion for large wavelengths is used to derive an analytical formula for the growth or decay rate of very wide fingers. A generalized mobility ratio, the sum of the mobilities of the two phases far behind the front divided by the sum far ahead, proves to be the first determinant of front stability: ratios larger than unity indicate instability and less than unity, stability. Gravity acting on the density difference between the phases is the second determinant. Incipient narrow fingers are always damped by capillary pressure gradient-driven flow. When the front is unstable there is a fastest growing wavelength, or width of incipient finger — a most dangerous mode. The growth rate of a given wavelength disturbance depends on its length in the flow direction. The greater that length, the faster growing a disturbance of given wavelength. Thus the results indicate that (1) stability depends on the dimensions of the reservoir or core being modeled, and (2) rate of development of fingering depends on the lengths of heterogeneities that disturb the flow.