The macroscopic pressure difference between two immiscible, incompressible fluid phases flowing through homogeneous porous media is considered. Starting with the quasi-static motions of two compressible fluids, with zero surface tension, it is possible to construct a complete system of equations in which all parameters are clearly defined by physical experiments. The effect of surface tension is then formally included in the definition of the specific process under consideration. Incorporating these effects into the pressure equations and taking the limit as compressibilities go to zero, the independent pressure equations are shown to yield indeterminate forms. However, the difference of the two pressure equations is found to yield a new process-dependent dynamical equation.