A general theory of electronic excitations in aggregates of molecules coupled to intramolecular vibrations and the harmonic environment is developed for simulation of the third-order nonlinear spectroscopy signals. The model is applied in studies of the time-resolved two-dimensional coherent spectra of four characteristic model systems: weakly / strongly vibronically coupled molecular dimers coupled to high / low frequency intramolecular vibrations. The results allow us to classify the typical spectroscopic features as well as to define the limiting cases, when the long-lived quantum coherences are present due to vibrational lifetime borrowing, when the complete exciton-vibronic mixing occurs and when separation of excitonic and vibrational coherences is proper.
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