It is demonstrated that the allowance for "axial" and "radial" — with respect to the direction of surface-wave propagation — inhomogeneities of plasma density, first, results in a variation of the spatial distribution of the electric field amplitude and, secondly, the frequencies of the propagating surface waves turned out to be local functions of the co-ordinates. The latter point is important in the interaction of charged-particle beams with surface waves. Indeed, the function ωsw() gives rise to a dependence of the phase velocity (vpn = ωsw/k) on the co-ordinates. Since the most intensive energy exchange between the beam and the surface wave occurs under Cherenkov resonance (vph = v0, where v0 is the beam velocity) the density inhomogeneity affects the conditions of resonance. For this reason, the growth rate of the unstable oscillations decreases.