We present a detailed discussion on infrared spectroscopy of vibrational combination bands and overtones of adsorbate systems. For the case that the (dynamical) lateral coupling between the adsorbates is dominated by dipole coupling, we present general results for the absorption spectra which can be used to analyze experimental data and deduce the bond anharmonicity delta omega. The theoretical results are used to analyze experimental line shape data for the combination band of the C-O and the Ru-CO stretch vibrational modes of CO adsorbed on Ru(001), as well as the overtone of the C-O stretch vibration for the same adsorbate system. It is found that for strong lateral coupling land weak anharmonicities) asymmetric line shapes are common; strong anharmonicities lead to the formation of localized two-phonon bound states besides a continuum of delocalized two-phonon states. However, even then the extraction of anharmonic parameters can be severely impeded by dynamic line shifts of the localized overtone band through virtual transfers of vibrational quanta to neighboring oscillators. We further consider the mechanisms which contribute to the broadening of overtone excitations and show that the energy relaxation rate for the overtone is twice as large as for the fundamental, while the (pure) dephasing rate is approximately four times higher than that of the fundamental excitation.