A method is presented for predicting the onset and stability character of nonaxisymmetric modes in liquid bridges and drops. The analysis applies to any fixed contact line axisymmetric interface in a steady force field. The onset and stability character of nonaxisymmetric equilibria in liquid bridges and drops is determined. Perturbation analysis is used to locate branches to nonaxisymmetry, and the configuration of the branches then gives the stability character. The number of unstable modes to both constant pressure and constant volume disturbances can be determined, so that changes in stability beyond the primary loss of stability may be examined. Although the first nonaxisymmetric mode tends to dominate higher order modes are significant for liquid bridges where length is less than radius and for drops at higher Bond numbers. At Bond numbers significantly greater than unity, the onset of the least unstable nonaxisymmetric modes tend to collapse between the fixed pressure and fixed volume axisymmetric modes of instability. For liquid bridges, two non-singular classes of nonaxisymmetric mode are distinguished: the predominant, classical shift mode; and a previously unreported tilt mode. The range over which the stability character of fixed contact line liquid bridges and drops is understood is significantly extended.