This thesis aims at the methodological developments in Nuclear Magnetic Resonance (NMR). The methodological developments in NMR has a long and successful history. The present thesis attempts to contribute some novel methods in this direction. This thesis restricts itself to two methodological developments, namely, (1) effects of cross-correlations between the chemical shift anisotropy (CSA) and dipole-dipole interactions in the relaxation of various nuclei and experiments which utilize spatial encoding. The cross-correlation has been successfully utilized to investigate the anisotropic motions of liquid crystals, and to understand the chemical shift anisotropy of fluorine atoms of Fluorine substituted ring compounds. Spatial encoding schemes have been developed to facilitate single scan measurements of longitudinal spin lattice relaxation times and implementations of parallel search algorithms.