Abstract: A cellulose dialysis membrane in the form of a hollow fiber is formed from cellulose-cuoxam solutions. An internal cavity is formed by a liquid or a gas. The membrane has a UFR of at least 4 ml/m.sup.2 . h . mm Hg. The hydrogel components of the cellulose are distributed in cells with a mean free path length of 3-10 nm in the membrane wall in a log-normal distribution. The mean free path length is the distance between the cells and is determined by the freeze-etching replica method after swelling of the membrane with water. More than 65% of all the hydrogel cell interfaces of the membrane have a form factor between 1.0 and 5.0. In addition, the UFR of the membrane after storage for more than ten days in a humid atmosphere at 20.degree. C. and 100% relative humidity is more than 50% of the value determined immediately after drying or after storage in a dry environment.