The line broadening in the electron resonance spectra of monoradicals dissolved in anisotropic media, such as liquid crystals, provides a valuable probe of both the orientational order and the molecular dynamics. However, the fast-motion relaxation theory employed to extract this information from the linewidths assumes that the nuclear spin is quantized along the direction of the magnetic field. This approximation is only correct when the symmetry axis of a uniaxial liquid crystal is either parallel or perpendicular to the field. We have therefore removed this assumption and have developed a general theory of line broadening valid for all orientations of the liquid crystal. The theory is then used to evaluate the angular dependence of the linewidths and this is compared with the dependence predicted by the approximate theory, for two classes of nitroxide spin probes. These comparisons reveal that for steroidal spin probes the error, introduced by assuming the nuclear spin to be quantized along the field, is confined to the dynamic properties derived from the linewidths. In contrast, significant errors appear in both the dynamic and static properties obtained from an analysis of the linewidth variations for fatty acid spin probes based on the approximate theory. It would seem that the exact theory must be employed to obtain precise information from linewidth investigations of liquid crystals, except when the orientational order is extremely small.