Three types of electrodialysis (ED) and electrodeionization (EDI) stacks are studied when treating NaCl solutions in the range of concentrations from 10(-5) to 3 x 10(-2) M: (1) with a non-conducting network spacer, (2) with a mixed ion-exchange monolayer bed, (3) with profiled membranes. The Sherwood number characterizing the desalination rate is measured in recirculation regime when the concentration of feed solution is slowly decreasing in time. The data obtained are compared with the results calculated and measured for "empty" desalination channels not containing any filling. It was established that the measured Sherwood numbers at overlimiting currents in stacks with filling are higher than that in "empty" channel under the same potential drop, while the latter, in turn, are higher than the Sherwood numbers calculated for limiting current density. The mass transfer rate in several cases (under 2.5 V par cell pair in diluted, <10(-4) M, solutions and high flow rates, >7 dm(3) h(-1) dm(-1), a stack with profiled membranes) may be 4 times higher than that in "empty" channel at limiting current density. The stacks with profiled membranes are shown to be effective in the overall range of concentrations. The stacks with non-conducting spacer can be used if the feed solution concentration is not too low, >2 x 10(-3) M in our experiments. The stacks with ion-exchange resins are more preferable in the case of treatment of strongly diluted solutions (e.g. at the second stage following an ED with profiled membranes), as well as in the cases where it is necessary to use a compact unit characterized by a low flow velocity, though the power consumption is slightly higher.