We have treated a nonequilibrium diffusion process where a solute is added to phases consisting of two immiscible solvents in a very long glass tube, for example. If we maintain the tube undisturbed, the diffusion will go on indefinitely. Whereas if we shake the tube in the middle, we will have the ordinary equilibrium case where the partition of the solute can be described by the partition constant, K. We have found theoretically that the long time limit of the concentration of the solute in the former nonequilibrium case becomes constant in each phase, and it will be shown that we can define a new nonequilibrium partition constant, K-D, that is related by the expression K-D = root D-1/D2K, where D-i in phase i = 1 or 2 is the diffusion coefficient. This predicts at least three new important implications in the text.