The propagation of the guided modes in a cylindrical waveguide with imperfectly conducting walls and with the radius having a weak harmonic variation in the axial direction is investigated using the expansion of the fields in terms of the ideal normal modes. The theory is applied to the design of a mode convertor that selectively transforms the power in the TEOrmode to the TEOsmode. The spectral response of the mode convertor is analysed and the possible improvements of the basic design of the mode convertor are discussed.