The spectral characteristics of surface plasmon resonance (SPR) in nanosized gold films were studied with method of internal reflection in the Kretschmann geometry. Using modulation polarimetry technique, we measured the spectral and angular characteristics of the parameter 2 2 fering in frequency and amplitude) is shown. The resonance parameters are determined and used for construction of dispersion curves ( ) k ω . Their interpretation is given based on the theoretical model for waveguide modes on both metal film surfaces that were proposed earlier.