Superconductivity in the two component model of coexisting local electron pairs (charged bosons) and itinerant fermions coupled via a charge exchange mechanism is discussed. The cases of isotropics‐wave and anisotropic pairing of extendeds‐wave anddx2−y2symmetries are analyzed for a 2D square lattice within the BCS‐mean field approximation and the Kosterlitz‐Thouless theory. The phase diagrams and superconducting characteristics of the model as a function of the position of the local pair (LP) level and the total carrier concentration, are determined. The model exhibits interesting crossovers from the BCS like behavior to that of LP’s. Finally, we analyze the pairing fluctuation effects (in 3D) within a generalized T‐matrix approach and determine the transition temperatures from the pseudogap state. © 2003 American Institute of Physics