This PhD thesis presents the results of electronic magnetic-circular-dichroism (MCD) and absorption spectroscopy of CH, NH, OH, PH, and SH isolated in various noble-gas (argon, krypton, and xenon) matrices (XH/NG) at cryogenic temperatures, using a high-resolution simultaneous MCD and absorption spectrometer, MOD4. Experimental problems prevented the study of CH/Xe, NH/Xe, or OH/Xe matrices. The results were interpreted in terms of a randomly oriented spin-orbit (SO) - crystal-field (CF) model previously developed by workers in this research group. SO and CF parameters were extracted by fitting the resulting data with parameterised equations derived from group-theoretical and quantum-mechanical considerations of the SO-CF model. In the cases of NH and PH, zero-field splitting (ZFS) parameters were also extracted. The SO-CF model worked well for CH, NH, and PH, but was found to fail for OH and SH. Trends in the parameters of XH with varying noble-gas host were attributed to the external heavy-atom effect and/or motional effects within the matrix. Preliminary attempts have been made to interpret spectral structure in terms of free or hindered rotation of the guest radicals within the host matrix. This has had a degree of success, especially for NH/Ar, however more theoretical work still needs to be done.