Abstract: A cross-counter-stream module for material and/or heat exchange done with a hollow filament bundle cast into a housing at its ends and a mechanism for conducting the material flow to the outside of the hollow filaments. The hollow filaments are cast at their ends as a stack into a housing, the stack being composed of one or more layers which consist of strata of hollow filaments fixed in a plane through cross-pieces transverse to their lumen directions, the cross-pieces being arranged tightly superimposed at all locations inside one layer, disposed at predetermined constant intervals, with the intermediate spaces between the hollow filaments filled by the cross-pieces at the places of crossing, and with the cross-pieces composed of a polymer with a melting point from 80.degree. to 190.degree. C. and a residual adhesion at room temperature. Preferably, the polymer is a polyamide, a polyethylene, a copolymer of polyethylene and vinyl acetate, or a copolyether-ester.