A method is presented for calculating the lowest cutoff wavenumber of a new microwave transmission line, the ‘T septate lunar line’. The T septate lunar line is a modified lunar line formed by two eccentric circular metal tubes; part of the inner metal tube is cut out, and a metal bar is passed through the cutout section to connect the opposing inner surfaces of the two tubes.The wave equation for the boundary-value problem associated with this complex waveguide form can be found by a perturbation method, using a cylindrical co-ordinate system. The cross-section of the T septate lunar line is approximated by introducing a series of steps in the outer guide wall and dividing the cross-section intomfan-shaped regions. The problem is thus reduced to one of a multiple-step waveguide. The solution of themstepped waveguide results in a system of 2mequations containing 2munknowns involving the cutoff wavenumber βcthe order of Bessel functionpithe angular parameter αiand the coefficient ratio parameter η1for the first composite region intersected by the inner metal tube. A successive approximation method is applied to obtain the cutoff wavelength. The calculated value is in close agreement with the experimental value.In the 200–2000Mc/s frequency band, the very compact and light T septate lunar line should find its greatest application in aircraft and space systems.