We report on selective separation of monovalent and divalent cations (Na+ and Mg2+) and anions (Cl- and SO42-) from aqueous solutions using the flow electrode capacitive deionization (FCDI) process, operated with ion-exchange and nanofiltration membranes (NF). For the selective separation of cations and anions the FCDI module was operated with an NF membrane (NF270) and an anion-exchange or cation-exchange membrane, respectively, at varying applied cell potentials (0.6, 0.8 and 1.23 V) and initial mono- to di-valent ions molar concentration ratios of 1, 10 and 20. The pennselectivity of the NF270 membrane, calculated as a ratio between measured ionic fluxes, was found highly dependent on the initial molar concentration ratios of the mono- to the di-valent ions. Concentration-normalized Na+ to Mg2+ perrnselectivity was 0.69-1.04, indicating that the NF270 membrane does not pose selectivity for the separation of sodium and magnesium in the studied process. Conversely, the concentration-normalized permselectivity between Cl- and SO42- was found between 1.28 and 7.03 depending on the applied cell potential, indicating high potential for implementing the proposed NF-FCDI method for selective separation of anions.