The influence of shear-spring + normal-spring type imperfect interface conditions on the dispersion of the generalized Rayleigh waves in a system consisting of a covering layer and a half-space with two-axial homogeneous initial stresses is investigated. The three-dimensional linearized theory of elastic waves in initially stressed bodies is employed and the plane-strain state is considered. The elasticity relations of the materials of the constituents are described through the Murnaghan potential and the influence of the third order elastic constants which enter the expression of this potential is taken into consideration. The corresponding dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results on the action of the parameters, which enter the formulation of the imperfect contact conditions, on the wave dispersion curves are presented and discussed. The results of these investigations can be successfully used for estimation of the degree of the bonded defects between the covering layer and the half-space.