The response of an intervalence band to an applied electric field, called an intervalence band Stark effect, is considered in detail. Because the application of an electric field to a symmetric mixed-valence complex will break its symmetry in a way that depends on the strength of the field and the orientation of the complex in the field, it is necessary to identify the most general treatment of the asymmetric vibronic coupling problem for the calculation of intervalence band Stark effects. For this reason three previous treatments of the asymmetric vibronic coupling problem are reviewed. Each treatment is found to be less appropriate for the calculation of intervalence band Stark effects than a fourth that we introduce. It is also shown that a common choice of vibrational basis in these treatments can lead to inaccurate calculations for some mixed-valence complexes; an alternative is recommended. Particular attention is paid to the effects of the field on the line shapes of intervalence bands and the sites of charge localization in mixed-valence complexes; both effects of the field lead us to identify intervalence band Stark effects as examples of a broader class of nonclassical Stark effects. A wide range of behavior for intervalence band Stark effects is predicted for isotropic samples. The Franck-Condon principle is utilized to develop a qualitative understanding of this behavior. Two methods of analysis are developed for determining the values of the vibronic coupling parameters that characterize a mixed-valence complex in the absence of the field from intervalence band Stark effects measured for isotropic samples; one of these methods can yield a complete description of the vibronic coupling parameters from an intervalence band Stark effect when the dipole strength of the intervalence band is either poorly characterized or poorly understood. The Stark effects of phase-phonon bands are also discussed. A graded description of charge localization in mixed-valence complexes is emphasized throughout this work, and a simple criterion for identifying the localized-to-delocalized transition is proposed.