The absorption of microwaves of frequency 9.58 GHz by binary mixtures consisting of polar molecules in a predominantly non-polar atmosphere was measured at pressures up to 260 bars. The polar molecules studied were CH3CI, NH3 and COS, and the non-polar molecules were H2, He, N2 and A. For the mixtures of CH3Cl or NH3 with H2 or He, it was possible to extend the measurements up to approximately 700 bars. The gas mixtures were contained in a tunable resonant cavity which was operated in the TE013 mode, and microwave radiation was transmitted through this cavity with the aid of coaxial coupling plugs capable of withstanding high pressures. An attenuator substitution method was then used for determining the power absorption coefficient of the gas. For all the gas mixtures studied, the power absorption coefficient increases with pressure up to the highest pressures reached.The inversion spectrum of NH3 was found to become non-resonant in the mixtures studied before the pressure reached 40 bars -- then, until the pressure reached at least 200 bars, the loss remained entirely non-resonant. In this pressure range the absorption data was described quite well by the formula of Cole and Cole (1941), and the mean relaxation rate seemed to be increasing very nearly linearly with density. Collision diameters obtained from this analysis were consistent with earlier findings. At the highest densities reached there was evidence that a transition to non-resonance in the rotational spectrum of NH3 had begun but had not advanced far.The rotational absorption in mixtures of CH3Cl or COS with H2 or He was well described by the Van Vleck-Weisskopf theory (1945) up to pressures over 200 bars - but at higher pressures it was excessive. For mixtures of CH3Cl or COS with A or N2 the measured rotational absorption was greater than that predicted by the Van Vleck-Weisskopf theory once the pressure exceeded approximately 40 bars; at 260 bars it was more than three times greater. These observations indicated that at least a partial transition to non-resonance in the rotational spectra of CH3Cl and COS had occurred. It was found that the difference between the measured rotational loss and that given by the Van Vleck-Weisskopf formulae increased as the square of density; hence the excess loss could be collision-induced absorption. It was also possible to fit the total measured rotational loss to the expression for microwave absorption given by Ben Reuven (1966). The collision diameters obtained from these analyses were very small.A reader who requires only a brief outline of the material contained in this thesis is referred to section I.1, section 1.6, section IV.4, the summary of the COS analysis (page 107), the summary of the CH3Cl analysis (page 113), and Chapter VI.