It is shown that the integrated absorption coefficients of strong fundamental bands of some gaseous substances can be determined with an accuracy of 5–10% using experimental data on the spectral moments of bands in the overtone spectral range of these substances in the liquid phase near the melting point. The absorption coefficients are calculated within the framework of the cell model of the liquid state from the contributions of the resonance dipole-dipole interaction to the second spectral moment. The combination and overtone absorption bands of the SF6, CF4, SiF4, NF3, CHF3, CC1F3, CBrF3, OCS, N2O, and CO2 molecules in the liquid state and in solutions in liquefied Xe, Kr, and O2 are recorded. The data in the literature on the intensity of strong IR bands in the gas phase are analyzed. Using an improved experimental technique, additional measurements are performed. It is found that the absorption coefficients determined from the spectral characteristics of the liquids agree well with the coefficients measured in the gas phase.