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The propagation characteristics of leaky waves on slotted circular cylinders are derived by the methods described in an earlier paper on leaky rectangular waveguides. The cross section of a typical leaky circular wavegaide is represented by a radial transmission line network incorporating a lumped terminating admittance which characterizes the slot discontinuity and the external region. The expression for the lumped admittance is obtained by combining an integral equation solution with a variational procedure. The resonances of this transverse network, which yield the complex propagation constants for the leaky waves, are solved by perturbation techniques to produce results in simple and practical form. Solutions are obtained for leaky waves corresponding to two different excitations of a slotted cylinder and these results are shown to compare favorably with measured values.