The Rh-Te and Ir-Te binary systems for 50-78 atom % Te show remarkable differences in their phase and structural features at temperatures below 1100 degrees C. Extended Huckel calculations are employed to investigate the influence of various orbital interactions on these differences. In general, a strong interrelationship among valence electron count, orbital characteristics at and near the Fermi levels, and relative strengths of M-Te, Te-Te, and M-M orbital interactions control the occurrence and structures of various MxTe2 compounds (0.75 less than or equal to x less than or equal to 2). Stronger Ir-Te than Rh-Te orbital interactions lead to the different low-temperature structures of IrTe2 (CdI2-type) and RhTe2 (pyrite-type), but then short and intermediate-range Te-Te interactions lead to the pyrite-type structure for the defect phases M1-uTe2. At temperatures above 600 degrees C, RhTe2 (pyrite-type) is unstable relative to disproportionation to the "stuffed" CdI2-type Rh1+xTe2 and the defect pyrite-type Rh1-uTe2. The Rh-rich phases, Rh1+xTe2, show ordered vacancies in alternating layers of octahedral holes and can be formulated as (Rh-3)(x)(Rh)(1-2x)Te-2 (x less than or equal to 1/2) and (Rh-3)(1-x)(Rh)(4x-2)Te-2 (x greater than or equal to 1/2) to emphasize the occurrence of linear Rh-3 units in their structures. The pattern of vacancies in these structures follows the preference of Rh4n+3 oligomers over Rh4n+1 chains. Charge-iterative calculations of Rh atomic orbital energies in Rh1+xTe2 (x = 0.0, 0.5, 1.0) were carried out to analyze the electronic properties of Rh throughout the series. As x increases, Rh-Te orbital interactions become less attractive and the concentration of Rh-Rh repulsive interactions grows. Both effects control the maximum value of x (observed to be 0.84) for this series and influence the pattern of occupied octahedral holes in the close-packed tellurium matrix.