This paper describes theoretical and experimental studies of the phase stab
ility in frequency-multiplying gyro-traveling-wave-tubes (gyro-TWTs). The t
heory is developed under assumptions that 1) an input waveguide operates in
a small-signal regime; 2) a drift region is free of microwaves; and 3) an
output waveguide can be analyzed in a specified current approximation, By u
sing these assumptions, one can develop an analytical theory describing the
phase sensitivity of frequency-multiplying gyro-TWTs. The calculations wer
e done for the parameters of a frequency-doubling gyro-TWT which was studie
d experimentally. In the experiments, the beam voltage and magnetic held ph
ase pushing factors were measured. The experimental results are in reasonab
le agreement with theoretical predictions. These results can be used for ev
aluating the restrictions on fluctuations in the beam voltage and current a
nd the magnetic held which should be fulfilled for providing a required lev
el of phase stability in gyro-TWTs.