The present invention provides polysulfone-based hollow fiber membranes having high water permeable performance and for use in therapy of chronic renal failures, said hollow fiber membranes having high safety and high stability in performance and being excellent in module-fabricating workability. The present invention also provides a process for manufacturing the same. The present invention relates to a bundle of a plurality of selectively permeable polysulfone-based hollow fiber membranes wherein the amount of a hydrophilic polymer eluting from each hollow fiber membrane is not larger than 10 ppm, and wherein the content of the hydrophilic polymer in the outer surface of the hollow fiber membrane is 25 to 50 mass %, and this bundle is characterized in that any of extracted solutions from ten fractions of said bundle, obtained by dividing the bundle at substantially regular intervals along the lengthwise direction, shows a maximum value of smaller than 0.10 in UV absorbance at a wavelength of 220 to 350 nm, with the proviso that the extracted solutions are obtained by the extraction method for tests regulated in the approval manufacturing standards for dialytic artificial kidney devices and in that the difference between the maximum and the minimum out of the maximum values of UV absorbance of the extracted solutions from the respective fractions is not larger than 0.05.
