Forced oil-water displacement and spontaneous countercurrent imbibition are crucial mechanisms of secondary oil recovery. The classical mathematical models of these phenomena are based on the fundamental assumption that in both these unsteady flows a local phase equilibrium is reached in the vicinity of every point. Thus, the water and oil flows are locally redistributed over their flow paths similarly to steady flows. This assumption allowed the investigators to further assume that the relative phase permeabilities and the capillary pressure are universal functions of the local water saturation, which can be obtained from steady-state flow experiments. The last assumption leads to a mathematical model consisting of a closed system of equations for fluid flow properties (velocity, pressure) and water saturation. This model is currently used as a basis for predictions of water-oil displacement with numerical simulations.