A systematic theoretical study of two PbTe-based ternary alloys, Pb1−xCdxTe and Pb1−xMnxTe, is reported. First, using ab initio methods we study the stability of the crystal structure of CdTePbTe solid solutions, to predict the composition for which rock-salt structure of PbTe changes into zinc-blende structure of CdTe. The dependence of the lattice parameter on Cd (Mn) content x in the mixed crystals is studied by the same methods. The obtained decrease of the lattice constant with x agrees with what is observed in both alloys. The band structures of PbTe-based ternary compounds are calculated within a tight-binding approach. To describe correctly the constituent materials new tight-binding parameterizations for PbTe and MnTe bulk crystals as well as a tight-binding description of rock-salt CdTe are proposed. For both studied ternary alloys, the calculated band gap in the L point increases with x, in qualitative agreement with photoluminescence measurements in the infrared. The results show also that in p-type Pb1−xCdxTe and Pb1−xMnxTe mixed crystals an enhancement of thermoelectrical power can be expected.