The transport (J) of waste products across dialyzer membranes is known to be proportional to the blood inlet concentration (Cbi) according to J = KCbi, where K is the clearance. For solutes present on both sides of the membrane, like sodium chloride, it has been shown that under certain conditions the transport rate will depend linearly also upon the dialysis fluid inlet concentration Cdi according to J = KbCbi -KdCdi. Kb and Kd are generalized clearances, which depend upon flow rates and membrane permeability but are independent of the concentrations. We have extended the results of Ross et al. in three ways. First, they only considered ultrafiltration (UF) that is equally distributed along the dialyzer. This is an unrealistic assumption, especially in hemodiafiltration and hemofiltration treatments with large UF rates (Quf) leading to large pressure drops along the dialyzer. Our approach allows for an arbitrary UF distribution. Second, it was possible to incorporate the more realistic model of Villaroel et al. for the local combination of diffusion and convection. Finally, we allow an arbitrary distribution of blood among the different fibers. All of these results are valid in both cocurrent and countercurrent configurations. With a sieving coefficient of 1, a good approximation for small solutes, we were also able to show that Kd = Kb - Quf, irrespective of the UF distribution along the dialyzer. This is an important result that, for example, provides a theoretical foundation for allowing a nonzero Quf in conductivity based clearance measurements.