A consistent pairing theory of carriers in real (r) and k space is developed. The pairing of different free (F), delocalized (D), and localized (L) carriers in r space leading to the formation of various bipolaronic states is considered within the continuum model and adiabatic approximation, taking into account the combined effect of the short-and long-range components of the electron-lattice interaction with and without electron correlation. We calculate the formation possibility of D and L bipolarons and determine their concrete formation criteria as a function of ϱ / 0 . The pairing scenarios of carriers in k space leading to the formation of different bipolarons ͑including also Cooper pairs or dynamic bipolarons͒ are considered within a generalized BCS-like model, taking into account the combined phonon-and polaron-bag-mediated processes. It is shown that the pure BCS pairing picture is the particular case of a more general BCS-like one, and Bose-Einstein condensation of r-space or ideal-Bose-gas bipolarons is irrelevant to the superconductivity phenomenon. The possible relevance of the results obtained to the high-T c superconductors is discussed in detail in the framework of a two-stage Fermi-Bose-liquid scenario of superconductivity that is caused by single-particle and pair condensation of attracting bipolarons.

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