The viscous surface conditions between two fluids are considered for fluid displacement in a homogeneous porous medium. The term viscous surface is defined here as a mathematical abstraction used to approximate the macroscopic shape of the boundary layer between two fixed saturations of displacing fluid by continuum theory. In the limit as the saturations approach each other, one then obtains a convergence of the viscous surface to a constant saturation contour. This yields a mathematical description of immiscible displacement in porous media which contains a theory of viscous fingering.