In this paper we use the recursion method and a linear muffin-tin orbital atomic-sphere approximation (LMTO-ASA) tight-binding (TB) Hamiltonian taken to first order in E-E, to obtain the electronic structure of Mo-Ru compounds and amorphous clusters of Mo1-xRux for several values of x. It is well known that the LMTO-ASA-TB formalism treats s, p, and d orbitals in an equivalent manner. Therefore it allows the inclusion of important effects, such as the splitting of the center of the bands due to local environment and s-p-d hybridization. These effects are often neglected in the usual parametrized tight-binding Hamiltonians. The LMTO-ASA-TB Hamiltonian used here is parametrized in the sense that potential parameters for the pure metals were used in the calculations and the relative position of the bands in the binaries was adjusted by imposing approximate charge neutrality. But the parametrization is based on a solid theoretical background and no fitting to more exact first-principles calculations is needed. In this paper we show that for the Mo-Ru compounds, a simple parametrized LMTO-ASA-TB Hamiltonian produces good results, when compared to independent first-principles, self-consistent augmented-spherical-wave k-space calculations. We also use the parametrized LMTO-ASA-TB Hamiltonian to obtain the electronic structure of amorphous Mo1-xRux alloys for several values of x. We show that, for these alloys, the density of states at the Fermi level, N(EF), tends to decrease as the Ru concentration increases. This is in agreement with observed experimental tendencies. We note that when the splitting of band centers and s-p-d hybridization are neglected in the calculations, the trends are reversed, with N(EF) increasing as the Ru concentration increases. This illustrates the importance of taking these effects into account. © 1990 The American Physical Society.