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Stimulated scattering induced by the longitudinal electric field of a pump wave is studied theoretically for the case of dense relativistic electron beams traveling in cylindrical metal waveguides. Two processes are examined. In one, the pump wave decays parametrically into a slow and a fast space‐charge wave. In the other, it decays into a slow space‐charge wave and a TM wave of the guide. The frequency characteristics and stimulated growth rates are given for each process, as a function of beam diameter, velocity, and density.