The electronic structure and superconductivity of layered organic materials based on the bis(ethylenedithio)tetrathiafulvalene molecule (BEDT-TTF, hereafter ET) with essential intra-ET correlations of electrons are analysed. Taking into account the Fermi surface topology, the superconducting electronic density of states (DOS) is calculated for a realistic model of K-ET2X salts. A d-symmetry of the superconducting order parameter is obtained and a relation is found between its nodes on the Fermi surface and the superconducting phase characteristics. The results are in agreement with the measured non-activated temperature dependences of the superconducting specific heat and NMR relaxation rate of central 13C atoms in ET. © 1998 John Wiley & Sons, Ltd.