Extracorporeal apparatus for selective removal of pathogenic factors, i.e. antigens, from blood by circulating the blood through hollow fibers which, exterior to the lumen are in proximity to antibodies, i.e. proteins having strong biospecific activity for the pathogenic factors. In some situations, the antibody is segregated in a liquid medium outside the hollow fiber to improve mass transfer and the antigen penetrates the ultrafilter wall of the fiber to join the antibody.