In a serpentine cylindrical waveguide the radius is constant and the centre varies harmonically in the axial direction about a straight line in a plane. The propagation of the guided modes in a weakly corrugated serpentine cylindrical waveguide with imperfectly conducting walls is investigated using the expansion of the fields in terms of the ideal normal modes. The selective interaction between two transverse electric modes is treated. The theory is applied to the design of a mode convertor that selectively transforms the power in the TEpqmode to the TEp+1,rmode. The spectral response of the mode convertor is discussed.