We investigate localized plasmon-mode resonances in the scattering and absorption of transversely polarized light by bimetal core-shell nanowires made of silver and gold, in two possible combinations, using an analytical solution and experimental data for metal permittivities. In particular, the influence of the metal shell thickness and material on these resonances is studied. We show that, unlike metal nanotubes with dielectric filling, bimetal wires do not display plasmon-mode hybridization.