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The model of superconductivity in the intercalated fullerenes based on arising of the valence bond between two neighbouring alkali-metal atoms is proposed. This model explains all the currently available experimental data concerning superconductivity in these compounds. Among them are the absence of superconductivity in A x C60 with even x, the dependence of the critical temperature on the disorder level and the carrier concentration, and the shape of the density of states near the Fermi level as a function of voltage in tunnelling spectroscopy.