Abstract: Process for production of a hollow fiber semipermeable membrane which can selectively separate the components of solution or gas mixtures, which consists essentiallly of dissolving cellulose triacetate and an organic acid and optionally a polyether in N-methyl-2-pyrrolidone to give a spinning solution having fixed contents of cellulose triacetate and organic acid and polyether (if any), and extruding the spinning solution through a spinneret into a gaseous atmosphere and immersing the spun fibers in an aqueous coagulation bath. The hollow fiber semipermeable membrane has excellent permeability and excellent separation characteristics with good life and hence is useful for various techniques such as dialysis, ultrafiltration, reverse osmosis, and separation of gases.