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Webster's simple bunching theory is extended to include the simultaneous oscillation of a reflex klystron at two or more frequencies. General expressions for the power and electronic admittance are derived that show the intermodulation effects of the oscillations upon each other. It is shown that in the presence of a vigorous low-frequency oscillation, oscillations may be obtained simultaneously at a higher frequency if the transit time is (n+1/4) r.f. cycles. The "normal" oscillations obtained for (n+3/4) r.f. cycles are shown to be usually unstable in the presence of the low-frequency oscillation. An analysis is given of the power and electronic admittances obtained when the oscillation frequencies are exactly in the same ratio as two integers. The theory is found to explain the intermodulation effects previously reported by the author.