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A rod with nonperiodically oscillated perturbation of surface impedance is considered. The Krylov-Bogoliubov-Mitropolsky asymptotic method is used for solving boundary-value problem describing electromagnetic wave propagation in the open waveguiding structure. Mutual transformations of a wave beam falling onto inhomogeneous impedance rod and two surface waves propagating along this rod are investigated. Analytical solutions for some particular cases are obtained.