The absolute limits of mass transfer across the membrane in a parallel-plate dialyser set by the flow pattern in both channels were determined on the basis of a mathematical model assuming axially dispersed plug flow. The lower limit corresponds to the case of mass transfer under laminar flow conditions. For determination of the upper limit for the same values of the parameters influencing the flow regime (e.g., flow-rate, mean residence time), plug flow and instant restoration of the transverse concentration uniformity, distrubed by the mass-transfer process, were assumed. This case corresponds to infinitely high Peclet numbers and mass-transfer coefficients (Sherwood numbers) in both channels. For a particular gross flow pattern in the channels (i.e. residence time distribution), characterized by non-zero axial dispersion, the lower limit will coincide again with the laminar case. However, the upper limit in such a case will correspond to infinitely high mass-transfer coefficients but finite Peclet numbers and will be lower than the absolute upper limit of the dialyser mentioned above. The results obtained allow the estimation of the range within which the mass transfer in real parallel-plate dialysers can be expected.