Two-dimensional (2D) electronic spectroscopy at cryogenic and room temperatures reveals excitation energy relaxation and transport, as well as vibrational dynamics, in molecular systems. These phenomena are related to the spectral densities of nuclear degrees of freedom, which are directly accessible by means of hole burning and fluorescence line narrowing approaches at low temperatures (few K). The 2D spectroscopy, in principle, should reveal more details about the fluctuating environment than the 1D approaches due to peak extension into extra dimension. By studying the spectral line shapes of a dimeric aggregate at low temperature, we demonstrate that 2D spectra have the potential to reveal the fluctuation spectral densities for different electronic states, the interstate correlation of static disorder and, finally, the time scales of spectral diffusion with high resolution. C 2015 AIP Publishing LLC.