The crystal structure of the new compounds of formula M₂CuSb₃ with M = Ti, Zr, Hf was found topologically parent to that of the tetragonal binary Cu₂Sb. However, a marked expansion of the c results in a distribution scheme for the different elements over various positions in the crystallographic unit cells. In all cases the electrical resistivity is of metal type with much higher values for this series of new compounds that contains a lower amount of copper. A spin and charge self-consistent KKR type of method was used to calculate the electronic structure of the M₂CuSb₃ intermetallics. The theoretical calculations support well a metal type conductivity. Further discussions on the electronic properties are based on the different contributions to the DOS at the Fermi level, arising from the different elements and their different sub-bands. By comparison to the reference compound Cu₂Sb, structural trends are proposed for a better understanding of the band structure peculiarities and the corresponding electrical resistivity characteristics.