Reports of long-lived exciton coherences have lead researchers to expect that model dimer systems inevitably generate exciton superposition states observable by two-dimensional electronic spectroscopy. Here we report a careful photophysical characterization of a model dimer system, a diacetylene-linked perylenediimide dimer to examine that issue. The absorption spectrum of the dimer shows molecular exciton splitting, indicating that excitation is delocalized. The assignment of exciton states was supported by other photophysical measurements as well as theoretical calculations. Ultrafast two-dimensional electronic spectroscopy was employed to identify and characterize excitonic and vibrational features, as they evolve over time. Population transfer between the two exciton states is found to happen in <50 fs, thus preventing the sustainment of exciton coherences. We show that such fast radiationless relaxation cannot be explained by coupling to a solvent spectral density and is therefore missed by standard approaches such as Redfield theory and the hierarchical equations of motion. (C) 2014 Elsevier B. V. All rights reserved.