The invention discloses a method for the production of a hollow fiber membrane module consisting of at least one strip-shaped mat with individual hollow fibers arranged next to each other in which method the mat is unwound from a first cylindrical winding core and then wound up onto a second cylindrical winding core in such a way that a wound-up hollow fiber bundle is formed whereby the second winding core is made up of at least one part. The method comprises the following steps: • transporting the mat from the first winding core in the direction of the second winding core at a variable speed vm whereby the mat rests on a carrier element that ....