In the present work, we give an analytical non-perturbative treatment of\nmode-mode coupling and anharmonicity occurring in molecular vibrational systems\nanalyzed by 2D-infrared spectroscopy. This analytical description allows a\ndetailed discussion of the intricate structure of the 2D-infrared spectra\nresulting from the contributions provided by the various possible chronological\norderings of the interactions with fields due to overlaps of the pulses. The\npeculiar role of the vibrational overtones and other combination states on the\nresonance shapes is elucidated and conditions for a better quantitative\nanalysis are discussed.\n