Dispersion of the generalized Rayleigh waves propagating in a covered half-space made of viscoelastic materials is investigated by utilizing the exact equations of the theory of linear viscoelasticity. The dispersion equation is obtained for, an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the dispersion of the waves under consideration. Dispersion curves are presented for certain attenuation cases and the influence of the viscosity of the materials is studied through three rheological parameters of the viscoelastic materials which characterize the characteristic creep time, long-term values and the mechanical behaviour of the viscoelastic material around the initial state of the deformation. Numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov. As the result of this discussion, in particular, how the rheological parameters influence the dispersion of the generalized Rayleigh waves propagating in the covered half-space under consideration is established.