The fundamental harmonic TE 01 gyrotron travelling wave amplifier (gyro-TWT) is a high-power, broadband, millimetre-wave amplifier with a low ohmic dissipation and a large guiding centre radius. However, spurious oscillations may reduce the amplification of the gyro-TWT. The stability of severed and distributed-loss gyroTWTs is analysed, using a self-consistent simulation code. A nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation (gyro-BWO) and reflective oscillation, is presented. Simulation results indicate that attenuating severs in the severed gyro-TWT do not suppress spurious oscillations, and that increasing the wall losses to suppress gyro-BWO in the distributed-loss gyro-TWT degrades the efficiency of the gyro-TWT amplifier. A multi-stage distributed-loss gyro-TWT design is developed to stabilize the amplification. The lossy and severed sections of the multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of absolute instability and gyro-BWO, respectively. The multi-stage gyro-TWT is predicted to yield a peak output power of 155 kW at 32.9 GHz with an efficiency of 15%, a saturated gain of 45 dB and a bandwidth of 2.2 GHz for a 100 kV, 10 A electron beam with an axial velocity spread Áv z /v z ¼ 5%.