Nuclear magnetic resonance (NMR) spectroscopy has been used since its inception to study chemical systems in the solid state. In general, these studies have dealt with measurements of relaxation times or interpretations of the NMR absorption spectrum in terms of the largest interaction present. However, the use of recently developed NMR techniques allows the separation and characterization of the interactions present. The work reported in this dissertation deals with the application of existing proton NMR techniques as well as the extension of high resolution techniques and their use to learn more about the nature and mobility of protons in H(,1.7)MoO(,3) and YH(,1.92);('*)DOE Report 1S-T-917. This work was performed under Contract W-7405-eng-82 with the Department of Energy.