The efficiency of natural light-harvesting complexes relies on delocalization and directed transfer of excitation energy on spatially well-defined arrangements of molecular absorbers. Coherent excitation delocalization and long-range molecular order are also central prerequisites for engineering energy flows in bioinspired devices. Double-wall cylindrical aggregates have emerged as excellent candidates that meet these criteria. So far, the experimental signatures of exciton relaxation in these tubular supramolecules could not be linked to models encompassing their entire spatial structure. On the basis of the power of two-dimensional electronic spectroscopy, we characterize the motion of excitons in the three-fold band structure of the bitu...