A theory is formulated for the displacement of a liquid from a porous system by another liquid, miscible with the first. In its most general form, the theory also may be applied to nonmiscible liquids. Differential equations are derived for the concentrations and fluxes of the two liquids as functions of time and distance in one‐dimensional flow. The equations are hyperbolic, in contrast to the equations encountered in earlier theories of miscible liquid displacement which are parabolic. The differential equations are solved for given boundary conditions. Some numerical examples illustrate the solution in the simplest case of miscible displacement.