Torrance et al. have made the interesting observation that several mixed-stack organic compounds undergo transitions from neutral states to ionic states as the temperature or pressure is varied. We examine a simple model of such transitions including Coulomb interaction and hybridization of neutral and ionic states. In the limit of weak hybridization and long-range repulsive interaction between ionic planes, it is proven that there is a complete devil's staircase where the degree of ionicity assumes an infinity of rational values. For attractive interactions between ionic planes, the neutral-ionic transition is shown to be first order for weak hybridization. Comparison with experiment indicates that this situation applies to tetrathiafulvalene chloranil. For strong hybridization the transition is continuous but goes through a metallic phase. It is shown, for the first time, that the spectrum of the charge-transfer Hamiltonian contains both a bound spectrum, the observed charge-transfer excitations, and a continuum. © 1983 The American Physical Society.