A new method has been used to remove oxygen impurities from selenium, which has made it possible to make relatively reproducible measurements of the electrical conductivity \ensuremath{\sigma} and the thermopower S of Se-rich alloys. We report the results of a brief study of ${\mathrm{Tl}}_{\mathrm{x}}$${\mathrm{Se}}_{100\mathrm{\ensuremath{-}}\mathrm{x}}$ alloys with x\ensuremath{\le}4 and a more extensive study of ${\mathrm{Se}}_{\mathrm{x}}$${\mathrm{Te}}_{100\mathrm{\ensuremath{-}}\mathrm{x}}$ with x in the range of 50 to 100. The Tl-Se results provide quantitative evidence for the removal of oxygen impurities from Se, and a quadratic dependence of \ensuremath{\sigma} on x is found which supports a model for the electrical behavior based on the presence of diatomic ${\mathrm{TlSe}}^{\mathrm{\ensuremath{-}}}$ ions. Over much of the experimental range of composition and temperature in the Se-Te alloys, \ensuremath{\sigma} and S have a behavior which conforms to a model of transport by holes at the mobility edge of the valence band, with a minimum metallic conductivity ${\ensuremath{\sigma}}_{c0}$ in the range from 10 to 40 ${\ensuremath{\Omega}}^{\mathrm{\ensuremath{-}}1}$${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.The transport data yield the distance of the Fermi energy ${E}_{F}$ from the mobility edge ${E}_{v1}$. With the help of bond equilibrium theory for the effects of bond defects, it has been possible to separate the effects of T and x on ${E}_{F}$ and ${E}_{v1}$, with the result that the large changes in ${E}_{F}$-${E}_{v1}$ are found to be mostly due to changes in ${E}_{v1}$ with x and T, rather than changes in ${E}_{F}$. At high T and at compositions approaching x=50, where the Maxwell-Boltzmann approximation is poor because ${E}_{F}$-${E}_{v1}$ is small, analysis based on Fermi-Dirac integrals yields quantitative evidence for the presence of a mobility edge, and a density of states which increases linearly with the hole energy. At x\ensuremath{\ge}80, the thermopower falls off and goes through a maximum with decreasing T. This behavior is analyzed in terms of added transport at energies above ${E}_{v1}$, but it has not been possible to account for it in terms of the expected behavior of localized states in the valence-band tail, simple donor or acceptor band states, or states at the conduction-band edge.