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We obtain the necessary and sufficient conditions for a two-component(2+1)-dimensional system of hydrodynamic type to possess infinitely manyhydrodynamic reductions. These conditions are in involution, implying that thesystems in question are locally parametrized by 15 arbitrary constants. It isproved that all such systems possess three conservation laws of hydrodynamictype and, therefore, are symmetrizable in Godunov's sense. Moreover, all suchsystems are proved to possess a scalar pseudopotential which plays the role ofthe `dispersionless Lax pair'. We demonstrate that the class of two-componentsystems possessing a scalar pseudopotential is in fact identical with the classof systems possessing infinitely many hydrodynamic reductions, thusestablishing the equivalence of the two possible definitions of theintegrability. Explicit linearly degenerate examples are constructed.Comment: 15 page

The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type