Femtosecond electronic relaxation dynamics of a cylindrical molecular aggregate are measured with transient grating (TG) and two-dimensional Fourier transform photon echo (PE) spectroscopies. The aggregates are double-walled cylindrical structures formed by self-assembly of amphiphilic cyanine dye molecules in water. The diameters of the inner and outer cylinders are approximately 6 and 10 nm. The linear absorption spectrum of the aggregate exhibits four spectrally resolved single exciton transitions corresponding to excited states localized on particular regions of the structure: (1) an excited state localized on the inner cylinder corresponds to the lowest energy transition at 16670 cm(-1); (2) a transition at 17150 cm-1 represents a state localized on the outer cylinder, (3) whereas an overlapping peak found at. 17330 cm(-1) is more closely associated with the inner cylinder; (4) an excited state delocalized between the inner and outer cylinder is assigned to a transition in the linear absorption spectrum at 17860 cm(-1). TG spectra show a series of resonances reflecting the electronic structure of both the single and double exciton manifolds. In addition, PE spectra reveal coherent modulation of both diagonal and cross-peak amplitudes persisting for 100 fs, where the coherence frequency matches the energy gap between transitions I and 4 in the linear absorption spectrum. PE line shapes suggest correlated energy level fluctuations for the exciton states associated with these two transitions, which is consistent with this fairly long-lasting coherence at room temperature in aqueous solution. The impact of these correlations on Forster energy transfer efficiency is discussed. The observations imply fairly long-range correlations between the molecular sites (>0.6 nm), which in turn reflects the length scale of the environmental motion inducing the fluctuations. We suggest that this environmental motion is most likely associated with water confined inside the cylinder and/or fluctuations of the dye's aliphatic functional groups.