Nonlinear gain in a 34 GHz, three‐stage, frequency‐doubling gyro‐traveling wave tube (gyro‐TWT) has been studied experimentally and theoretically. The device consists of a thermionic electron gun, TE01→TE02fundamental gyro‐TWT input section, second harmonic TE03intermediate buncher section, and a second harmonic TE02→TE04complex output circuit. In this study, the complex harmonic transfer characteristics were experimentally measured and compared with calculations based on the assumption that the gyro‐amplifier gain can be described, in the narrowband sense, as a classical frequency doubling circuit. The results show that narrowband intermodulation gain is 6 dB higher than the carrier as predicted in the small signal limit, but as the device reaches saturation the nonlinear products become suppressed with respect to the carrier. Tests on the noise gain characteristics show that output noise consists of second harmonic shot noise spontaneously excited in the output circuits along with product modulation between external noise and the carrier. Good agreement between the experimental results and the calculations is demonstrated. © 2003 American Institute of Physics