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The circular-electric-mode hybrid coupler permits electromagnetic energy to be transferred from a circular waveguide, which supports a TE01 mode, to a coaxial waveguide also supporting a TE01 mode, or vice versa. The extent to which this transference occurs is controlled by a cylindrical-waveguide `drift¿¿ region, which supports both a TE01 and a TE02 mode. The coupling mechanism is closely analogous to that which occurs in the more familiar rectangular-waveguide hybrid, or Riblet, coupler. The paper provides a theoretical description of such a coupler, the results of which are shown to be in agreement with measurement. The theory represents a new application of the moment method.