The work described in this thesis is principally concerned with the measurement of the anharmonicity associated with 'isolated' CH stretching frequencies, and the prediction of individual bond dissociation energies from these values. In addition, CHC1F₂ was the subject of an extended anharmonic vibrational analysis, and CHD₂C1 of a similar vibration-rotation one. In the first of these studies, the IR gas phase spectra of the two isotopic species: CH³⁵C1F₂ and CH³⁷C1F₂, were recorded in the range 15000 - 300 cm^-1. The frequencies of all fundamental vibrations have been accurately determined and analysis of the 800 cm^-1 region Fermi resonance dyad between v4 and 2v6 by the method of isotope shifts yielded an initial estimate of the k₄₆₆ potential energy term. This value enabled the complex pattern of 'hot' bands observed here and in the 1200, 1400, 1600 and 2000 cm^-1 regions, where related Fermi resonances occur, to be analysed, yielding several X<i>ij</i> (i,j = 4,5,6,9) values for both isotopic species. An initial refinement calculation on the data for the ³⁵C1 species from these regions resulted in more accurate X_ij values and a superior estimate of K₄₆₆. A subsequent refinement using data up to 10000 cm^-1 for the vibrational modes v1, v4, and v6 enabled further X_ij (i,j = 1,4,6) values to be determined and several features associated with the CH stretching overtones to be successfully explained. However, the unexpected doublet observed in the region of the CH stretching fundamental could not be unambiguously assigned beyond that one component results from a 'hot' transition. Finally, several more X_ij values were determined from the many overtone and combination bands of other vibrational modes observed in this study, thus defining in total 32 of the 45 anharmonicity constants for this molecule. Secondly, the CH stretching and CH bending modes, their overtones and combinations, in a series of tri-halogenated methanes were studied. The observed spectral features of interests were explained by application of simple second order perturbation theory. However, this approach failed to account for the spectra above approximately 10000 cm^-1 at which point it apparently becomes necessary to apply first order perturbation theory. During the course of this study several ωi and X_ij values were determined. In addition, the inclusion of terms of the type ωey_evi + 1/2)³ when treating an 'isolated' CH bond in a polyatomic molecule as a simple diatomic was investigated. In the next two groups of studies the technique of partial deuteration was employed in order to obtain information on individual CH bond strengths in methyl groups. Firstly, some molecules having symmetrical methyl groups are discussed, specifically CHD₂X (X = C1, Br, I). For the bromide and the iodide the CH stretching mode, v1, and its first two overtones were recorded whilst the entire spectrum of the chloride in the region 12000 - 400 cm^-1 was observed. The bands of these compounds are amenable to both rotational and vibrational analysis in many instances. Thus, for each molecule a value of A_o was determined along with the anharmonicity constant X₁₁. In CHD₂C1 the analysis led to a number of harmonic frequencies, ωi.