The possible existence of superconductors with high transition temperatures is analyzed for both the ordinary electron-phonon interaction and nonphonon superconductivity mechanisms. The existence of such systems depends on a negative static dielectric permittivity. The possible occurrence of this situation for an electron-ion system is analyzed. It is shown that negative values of the static dielectric permittivity are possible in the case of strong local-field effects, i. e., in the case of exchange-correlation interactions in the electron subsystem or the localization of point ions for an electron-phonon system. Equations for the transition temperature of strong-coupling superconductors are analyzed. Restrictions imposed on the transition temperature by the equations themselves and by the conditions for stability of the material are examined.