We report on surface-enhanced Raman scattering (SERS) activity of bimetallic core-shell Au@Ag nanorods. These nanostructures feature four plasmon maxima in the UV-visible range. Their application for SERS analysis enables matching individual optical properties of organic analytes using the optimal excitation wavelength resonant both for plasmon nanostructures and analytes. It promotes higher sensitivity of surface-enhanced resonance Raman scattering (SERRS) of specific analytes. The intensity of SERRS spectrum is higher up to 2 orders of magnitude for alizarin and up to 4 times for malachite green as compared to the corresponding SERS spectra. Thus Au@Ag nanorods can be used as a single SERRS substrate for sensitive analysis of a number of dyes.