Superconducting pairing mediated by antiferromagnetic (AFM) exchange and spin‐fluctuations is considered within the effective two‐band Hubbard model for a copper‐oxide plane. It is proved that retardation effects for the AFM exchange induced by interband hopping are unimportant that results in pairing of all the carries in the conduction band and highTcproportional to the Fermi energy. The kinematic interaction induced by intraband hopping gives an additional spin‐fluctuation contribution to thed‐wave pairing.Tcdependence on pressure and oxygen isotope effect are explained. © 2003 American Institute of Physics