This paper describes theoretical and experimental studies of the phase stability in frequency-multiplying gyro-traveling-wave-tubes (gyro-TWTs). The theory 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 using these assumptions, one can develop an analytical theory describing the phase sensitivity of frequency-multiplying gyro-TWTs. The calculations were done for the parameters of a frequency-doubling gyro-TWT which was studied experimentally. In the experiments, the beam voltage and magnetic field phase pushing factors were measured. The experimental results are in reasonable agreement with theoretical predictions. These results can be used for evaluating the restrictions on fluctuations in the beam voltage and current and the magnetic field which should be fulfilled for providing a required level of phase stability in gyro-TWTs.