We present the results of studies of a gyroklystron with the TE 53 output mode. A 30-dB gain is obtained at a frequency of 30 GHz for an output power of 5 MW, efficiency 25%, pulse duration 0.4 ms, and amplification bandwidth 40 MHz.1. At present, the development of multimegawatt gyroklystrons is mainly aimed at the international program of creating new-generation electron-positron colliders [1]. The majority of such gyroklystrons [2-6] use the TE 01 or TE 02 modes as operating ones for which the axisymmetric electric field on the cavity wall is zero, which is favorable from the electric-strength viewpoint. However, such modes fail to eliminate the risk of thermal "fatigue" of the cavity walls in the pulsed-periodic regime. Moreover, the TE 0p modes (with axisymmetric fields) compare unfavorably with modes of other types if the radial index p increases. Therefore, the high-order TE mp modes with nonzero azimuthal indices m, which have long been used in gyrotrons [7], are rather attractive. Both electric and magnetic fields of such modes on the cavity walls are relatively small compared with the fields in the zone of interaction with the electron beam.The possibility of creating a high-order nonsymmetric-mode gyroklystron is supported by the results of our previous studies such as development of the method allowing us to reach a high-frequency electricfield intensity of 150 kV/cm on the electrodynamic-system wall [8], creation of a magnetron-injection gun forming a helical electric beam (with an accelerating voltage of 280 kV and a current of 60 A) with a pitch factor of 1.3 for the case of acceptable electron spread over transverse velocities [9], and testing the output cavity in the active-oscillator mode where the output power exceeding 10 MW is obtained at a frequency of 30 GHz for the TE 53 mode and the radiation duration equal to the supply-voltage duration [10,11]. 3 4 5 2 1 7 10 8 9 6 Fig. 1. * zaitsev@appl.sci-nnov.ru † Deceased.