According to Buckingham's theory on solvent effects the shift caused by solute-solvent interaction should be linearly proportional to the vibrational quantum number of the excited vibrational level which is involved. In order to provide an experimental check on this theory we measured the wave numbers of the OH, NH, or CH fundamentals, their first and second overtones of phenol, 2,6-di-tertiary-butyl-4-methylphenol, N-methylaniline, and chloroform in a series of nonpolar or weakly polar solvents. The results indicate that the agreement with experiment is satisfactory for 2,6-di-tertiary-butyl-4-methylphenol and for phenol in the most weakly associating solvents but not for phenol in more strongly associating solvents, or for N-methylaniline, or chloroform. Buckingham's theory in its original form uses second-order perturbation techniques. We tried to improve the agreement between theory and experiment in taking account of the off-diagonal matrix elements of the quartic potential constant. This way we were able to interpret the main trends observed in the spectra but the need for higher approximations is still indicated. The spectra of 2,6-di-tertiary-butyl-4-methylphenol were also measured at −78°C and, in a solid glass, at −190°C. The observed changes can be interpreted in terms of increased solute-solvent interactions becoming more significant at liquid air temperature.