Abstract. The electronic structures of the two thermoelectric materials Bi 2 Te 3 and Bi 2 Se 3 are studied using density-functional theory with the spin-orbit interaction included. The electron states in the gap region and the chemical bonding can be described in terms of ppσ interaction between the atomic p orbitals within the 'quintuple' layer. For Bi 2 Se 3 , we find both the valenceband maximum as well as the conduction-band minimum, each with a nearly isotropic effective mass, to occur at the zone centre in agreement with experimental results. For Bi 2 Te 3 , we find that the six valleys for the valence-band maximum are located in the mirror planes of the Brillouin zone and they have a highly anisotropic effective mass, leading to an agreement between the de Haas-van Alphen data for the p-doped samples and the calculated Fermi surface. The calculated conduction band, however, has only two minima, instead of the six minima indicated from earlier experiments. The calculated Seebeck coefficients for both p-type and n-type materials are in agreement with the experiments.