A support structure for a bioreactor has a porous membrane (2) and a first textile structure (4) which is located in the direct proximity of said membrane. A second fabric (3) is located directly on the membrane (2), lying therefore between the membrane (2) and said first textile structure (4). This second fabric (3) has a considerably finer structure than the first textile structure (4). The provision of the additional fabric (3) detaches the accumulation of cells (6) from the membrane (2) and as a result, there is no diffusion resistance for these cells (6) on the textile surface. This improves the supply of nutrients locally, the adherence of the cells (6) in the respective wide-meshed intermediate area (5) being optimised.
