Linear Colliders operating in the 0.3 TeV to 1 TeV energy range may be optimally driven at a microwave frequency near 10 GHz. Assuming the use of 16 X pulse compression circuits, the required microwave amplifer tubes would need to have pulse duration ~ 2 μs, and peak power rating of 25 to 50 MW for each collider port (100 to 200 MW if one tube is to be used for four ports). To test the feasibility of meeting these requirements, a study of a 36 MW, 10 GHz, TE°01 mode, 4-cavity gyroklystron is in progress. The tube employs a 1.5 μs, 160 A, 500 kV magnetron injection gun which has been designed for relatively modest values both of cathode loading (5.6 A/cm2) and of field at the electrodes (< 91 kV/cm). The self-consistent circuit analysis considers all important effects including: fringing fields in the drift spaces, electron velocity spread, and space charge depression of electron energy. The values of cavity Q factors, and the dimensions of the cavities and the drift spaces are optimized for stability and for maximum efficiency. It is calculated that the amplifier will have saturated efficiency of 45.5% and saturated gain of 63 dB. Modulator construction and cavity cold testing have been completed, and a laboratory demonstration of this amplifier is expected in calendar year 1987. Finally, prospects for scaling X-band gyroklystrons to peak power levels of 100 to 200 MW, and phase stability of gyroklystrons are discussed.