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The extinction spectra of two-layered gold nanowires (TGNWs) have been calculated by using the vector wave function method. When the polarization direction of incident light is perpendicular to the incidence plane, it is found with increasing the incidence angle that the dipole resonance wavelength of TGNW shows a decrease, whereas the full-width at half-maximum (FWHM) for the dipole resonance peak decreases. With decreasing the shell thickness or increasing the dielectric constant of the inner core, the localized surface plasmon resonance (LSPR) of TGNW shows a distinct redshift, whereas the FWHM of the dipole peak increases. When the polarization direction of incident light is parallel to the incident plane, the LSPR in TGNW gradually appears with decreasing incidence angle and can be modulated by the geometry. We have ascribed the variations of the LSPR in TGNW to the competition between the variations of phase retardation and oscillation electrons. [ABSTRACT FROM AUTHOR]