High frequency (⩾ 200 GHz) gyrotrons are potentially useful for several important applications, including plasma heating and radar. For electron cyclotron resonance heating of a moderate-size, high power density tokamak power reactor to ignition temperatures, a gyrotron frequency around 200 GHz appears to be necessary. The design of high frequency gyrotrons is discussed. Analysis of overall gyrotron efficiency indicates that high efficiency may be obtained in fundamental electron cyclotron frequency (ω c) emission at high frequencies. The linear theory of a gyrotron operating at the fundamental frequency is derived for the TE mpq modes of a right circular cylinder cavity. An analytic expression is given for the oscillator threshold or starting current versus magnetic field.