The dispersion curve for the first generalized Rayleigh mode on the surface on an anisotropic substrate covered with an anisotropic layer is calculated. We show that, for directions in which both the Rayleigh and leaky Rayleigh waves can propagate on the uncovered substrate, the dispersion curve of this generalized mode splits into two branches at a certain value of the product of the wave number and the thickness. This splitting has to be taken into consideration when deriving layer properties from dispersion curves. For the derivation, we considered the anisotropic layer as a perturbation of the anisotropic substrate. An efficient computer program based on the extended Tiersten approach was written to numerically calculate the phase velocity as a function of frequency. (C) 1996 American Institute of Physics.