The synthesis of the new ternary hafnium tellurides Hf(5)MTe(3) (M = Fe, Co) and Hf(8)MTe(6) (M = Co, Ni, Ru) is reported. The single-crystal structure of Hf5FeTe3 has been determined. Hf5FeTe3 crystallizes in the orthorhombic space group Pnma (No. 62) with lattice parameters a = 17.837(1) Angstrom, b = 3.7044(5) Angstrom, c = 13.183(2) Angstrom (Z = 4); the lattice parameters for the Co analog show a slight shortening of all axes : a = 17.805(4) Angstrom, b = 3.698(2) Angstrom, c = 13.165(6) Angstrom. The single-crystal structure of Hf8FeTe6 has also been determined. Hf8FeTe6 crystallizes in the orthorhombic space group Pmmn (No. 59) with lattice parameters a = 25.815(5) Angstrom, b = 3.7309(7) Angstrom, c = 7.598(1) Angstrom (Z = 2); the lattice parameters for the new Co, Ni, and Ru analogs are reported. M-centered, tricapped, trigonal prisms of hafnium constitute the basic structural unit of both sets of compounds, and in both structure types these clusters condense to form one-dimensional chains. The more metal-rich composition of Hf(5)MTe(3) is achieved through edge sharing of clusters within such chains to form double chains. Tellurium coordination is nearly identical in Hf5FeTe3 and Hf8FeTe6, producing strikingly similar channels that run parallel to the b axis. Four-probe resistivity measurements show metallic behavior for Hf5FeTe3, in accord with electronic structure calculations. These calculations also show that Hf-Fe bonding is of primary importance in stabilizing this structure type.