We report results of electrical-conductivity, thermoelectric-power, and optical experiments on single crystals of Ni1-xCoxS2 (0x0.12). The results cannot be explained by means of a conventional one-electron model. However, if it is assumed that both strong electronic correlations and strong electron-phonon coupling exists for electrons in the narrow d bands associated with the transition-metal cations, the experimental results can be understood quantitatively. In the model presented, NiS2 is a Mott insulator, in which the gap is due to a correlation splitting of the 3d-eg band. The introduction of Co substitutionally for Ni results in one hole per Co atom in the lower of these bands. However, strong electron-phonon coupling leads to small-polaron formation, and thus a drastic band narrowing with increasing temperature. For this range of x, the d-band holes conduct only by means of thermally activated hopping for temperatures above 100 K. Screening effects due to thermally excited carriers lead to a collapse of the energy gap at a critical temperature, but small-polaron hopping remains the predominant conduction mechanism. © 1980 The American Physical Society.