The static and time-resolved optical response of 5,5′,6,6′-tetrachlorobenzimidacarbocyanine chromophore-based tubular double-wall molecular aggregates is studied. The linear dichroism and absorption spectra have the same basic structure for all aggregates investigated essentially showing a set of narrow and highly polarized bands originating from inner and outer wall excitations. The exact positions and strengths of absorption bands are influenced by the choice of side groups and various additives. Time-resolved fluorescence measurements show a substantial speeding of the fluorescence decay upon aggregation, mainly resulting from collective effects. Pump-probe experiments evidence slow inner-to-outer and fast outer-to-inner wall energy transfers between the walls of the tubules.