The aim was to extract alpha-lactalbumin (alpha-LA) selectively from acid casein whey protein concentrate (WPC) at pH 7 by limiting beta-lactoglobulin (beta-LG) transmission. In order ts achieve a high selectivity (ratio of alpha-LA transmission/beta-LG transmission), inorganic membranes were chemically modified by a polyethyleneimine coating bearing positive charges. In-depth study by anion-exchange chromatography with a similar polymer coating permits to expect a more selective ion-exchange process with beta-LG by the membrane at low or moderate ionic strength. Accordingly, transmission was investigated versus ionic strength (NaCl added) : transmission of beta-lactoglobulin was lowered with the modified membrane (alpha-LA transmission about 10%) and selectivities close to 10, were achieved at low ionic strength (I less than or equal to 0.02 mol l(-1)) when unmodified membrane selectivities were about 3 whatever the molecular-weight cut-off be. High selectivity of the tailor-made membrane was due to the adjustment of molecular sieving combined with anion-exchange interactions between negatively charged beta-LG and the membrane, the reversible fouling of which was enhanced. Modification of the net charge of protein by specific adsorption of divalent ion such as calcium or phosphate increased or decreased the transmission of protein, respectively, but the membrane selectivity was similar because the adsorption of divalent ion occurred on the two proteins.