Three different types of new ternary stannides and antimonides have been recently synthesized and investigated for their structural and physical properties, and systematically analyzed in terms of band structure determination. These materials are formed with an early d-metal such as Ti, Zr, Hf (as well as Sc for a part), a late d-metal such as Co, Ni, Cu, and X being Sn or Sb. The crystal structure analyses show that they crystallize either with a derivative Cu₂Sb, or a TiNiSi or mostly with the MgAgAs (semi-Heusler) type structure. Strong covalent bonding are evidenced from this analyses. The band structure calculations reveal that the late d-metal bands do not contribute significantly to the conduction, but the conductivity (if any) issues from the d- or p- type electrons of the early d-metals. This allows to control fairly the opening a gap (or semi-gap) at E_F via the VEC, and to initiate interesting thermo-electric properties.