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A theoretical analysis of auto-tuning systems for actively operated hydrogen (H) masers is presented. Tuning procedures based on changes in the frequency or the phase of oscillation are considered and compared. The analysis takes into account the basic results of sampling theory. The condition which should be satisfied when the reference frequency source is perturbed by white or flicker phase noise is specified. It is shown that the phase method should give better results than the frequency method when the reference source is a good quartz crystal oscillator.