The invention relates to a hollow fiber bundle for accommodation in a mass transfer device, the hollow fiber bundle including a multitude of hollow fiber strands for heat transfer and/or mass transfer which are aligned essentially at least locally along a preferential direction and are arranged with respect to one another in relation to their local preferential directions such that at least one first group of hollow fiber strands points essentially in a first preferential direction, at least one second group of hollow fiber strands essentially in a second preferential direction and at least one third group of hollow fiber strands in essentially a third preferential direction, the three preferential directions being independent of one another.