摘要： Many physical systems exhibit behavior associated with the emergence of the so-called rogue waves which represent dramatically high-amplitude events that occur with low probability but much more frequently than expected in ordinary wave statistics [1]. For example, in laser physics and optics rogue waves arise in the process of supercontinuum generation and represent pulses of ultra broadband light with extremely high peak power [2]. In this paper within the framework of the average approach and in direct 3D PIC (particle-in-cell) simulations we demonstrate that rogue waves can also appear in gyrotrons operating with high excess over the threshold. The mechanism of extreme spikes formation is related to simultaneous cyclotron interaction of a gyrating electron beam with forward and backward waves near the waveguide cutoff frequency as well as with the longitudinal deceleration of electrons. From the practical point of view, experimental observation of the rogue waves generation in gyrotrons can be interesting as a method for production of high-power millimeter-wave radiation with an ultra broadband spectrum. The required exceeding over the threshold can be achieved for routine parameters of the driving electron beams formed by the magnetron-injection guns due to operation at the lowest modes of microwave cavities.