a b s t r a c tElectronic structures of orthorhombic ternary nickel silicides: superconducting Lu 2 Ni 3 Si 5 and its nonsuperconducting counterpart, Y 2 Ni 3 Si 5 , have been calculated employing the fully relativistic and fullpotential local-orbital method within the density functional theory. Our investigations were focused particularly on the band structures and Fermi surfaces (FSs), being very similar for both ternaries. It appears that their FSs exist in four bands and contain electronlike and holelike three-dimensional sheets and small pockets, which suggests a presence of two-or even multi-band superconductivity (SC) in Lu 2 Ni 3 Si 5 . The main difference between both systems is that only in Lu 2 Ni 3 Si 5 small electron FS pockets occur around the G point. It allows for arising BCS-like SC in this compound, as was deduced from previous heat-capacity measurements, while no sign of SC has been detected (at least down to 2 K) in Y 2 Ni 3 Si 5 . In the latter system, a possible formation of a ferromagnetic ground state, which usually tends to destroy SC, has been excluded by our calculations.