Measurements of the rejection of perchlorate anion (ClO4-) were performed using nanofiltration (NF) and ultrafiltration (UF) membranes. Aqueous solutions of perchlorate (at a concentration of 100 mug/L of ClO4- by "spiking" with KClO4) were fed to the membrane test apparatus. Solutions contained only perchlorate, or an additional salt (KCl, K2SO4, or CaCl2) at overall ionic strengths of 30,60, or 115 mS/cm, and pH adjusted to 4, 6, 8, or 10. The data were modeled by application of a non-equilibrium thermodynamic model. The model has five parameters: the molecular transport coefficient (omega), osmotic pressure gradient (DeltaPi), molecular reflection coefficient (sigma), the average bulk fluid interfacial concentration between the feed and permeate side (C-avg), and the solvent flux (J(nu)). These parameters were determined by independent measurements (and calculation with minimum assumptions.) For example, the molecular transport coefficient (omega) was obtained by diffusion cell measurements under varying pH and conductivity conditions - generally it decreased with increasing pH and increased with conductivity for the membranes in our study. Measured and predicted perchlorate transport was in good agreement. Overall, the results indicate that, in a pure component system, target ions (in this case ClO4-) can be excluded from (negatively) charged membranes with pores large with respect to the size of the ion, but this rejection capability is quickly lost in the presence of a sufficient amount of other ions that can screen the apparent electrostatic force field. As intuitively expected, the perchlorate flux is governed by convection in large pore membranes.