A series of high power, high efficiency Ä^-band and W-band gyroklystron experiments has been conducted recently at the Naval Research Laboratory (NRL). Stagger tuning of the cavities for bandwidth enhancement is commonly used in the conventional multicavity klystrons. The desired stagger tuning is usually achieved via mechanical tuning of the individual cavities. However, in the millimeter wave regime, particularly, in the case of the high average power operation, it is desirable to be able to achieve the required stagger tuning by design. The NRL gyroklystron experiments explored the tradeoffs between power, bandwidth, efficiency, and gain to study the effects of large stagger tuning in millimeter wave without resorting to mechanical tuning of the cavities. Both, K^-band and W-band, experiments demonstrated a record power-bandwidth product. The success of the experiments was due in large part to a battery of improved large-signal, stability, and cold test codes employed in the modeling and design stage. Theoretical models that provide the basis for these design simulation tools and the design methodology will be presented. © 7999 American Institute of Physics. [S1070-664X (99)