A two-component theory of superconductivity is developed where one electronic component provides mobility and the other provides pairing. For the Cu-O-based high-T(c) materials the two components are identified with mobile electronic states associated with Cu-O planes, and localized negative-U states associated with oxygen vacancies in the Cu-O planes. An explicit comparison of phenomenology with BCS theory is performed including comparison with experiments on YBa2Cu3O7. The discussion includes quantitative comparison of the superconducting properties T(c), DELTA, H(c), and xi. Long-wave collective excitations, normal-state properties including resistance and tunneling and the isotope shift are described. Unusual properties are predicted including neutral fermion excitations, a spreading of the fermionic gap onset, a separation between the resistive transition T'c and the evaporation of the condensate T(c), anomalies in sound and bulk modulii at T(c), linear temperature dependence of normal-state resistivity, linear voltage dependence in normal-state tunneling conductance, and finite zero-bias conductance in superconducting-state tunneling. A new signature of structural coherence obtained by channeling experiments is indicated.