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The stable operation of a high-repetition-rate dispersion-tuned harmonically mode-locked fiber-optical parametric oscillator (FOPO) is demonstrated for the first time to the best of our knowledge. The experimental results match well with the theory. By introducing large cavity dispersion, the round-trip delay can vary with wavelength. Thus the cavity can be synchronized with the modulation frequency of an external clock passively. The FOPO can be tuned simply by adjusting the modulation frequency. A stable 10-GHz pulse train is obtained over 6-nm tuning range for each of the signal and idler.