This thesis is devoted to electron spin resonance studies of organic radicals in the solid and liquid phases. In the former state, anisotropic dipolar interactions are obtained and interpreted whilst in the letter state, the entirely unconnected phenomenon of linewidth alternation is considered. The work on iminoxy-radicals in the solid state showed that the isotropic interaction of the spin density on the iminoxy-group is greater with cis-substituents. The sign of isotropic hyperfine couplings was determined for those nuclei whose anisotropic hyperfine couplings could be both measured and predicted. Information was also obtained about the conformation of unsymmetrical iminoxy-radicals in the solid state. The results from frozen solutions of nitro-anions gave the value of the spin density on nitrogen, and the change in hybridisation of the nitro-group was given as a function of this spin density. The number of nitrogen interactions observed in the solid-state spectra of polynitro-radicals was correlated with the data for these radicals in fluid solution. Frozen solutions of nitrogen heterocyclic radicals were used to obtain a purely experimental value of the spin density on nitrogen, and hence, obtain various parameters by a method independent of the value of the other II parameters. The isotropic spectra of the anions of o-dinitro-benzene and m-dinitrobenzene in 1,2-dimethoxyethane were simulated to identify the radicals and obtain splitting constants accurately. This involved the prediction of the relative broadening of lines in the spectrum, a task which was performed in two ways, both of which could readily include several sets of nuclei whose isotropic hyperfine splittings were modulated. The species involved were discussed, and processes which could produce the modulation of isotropic hyperfine interactions were suggested. It was shown that the relative signs of the modulated splittings could be obtained from spectra broadened by slow modulation of these splittings.