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We have measured the current-voltage characteristics of overdamped long YBa/sub 2/Cu/sub 3/O/sub 7/ biepitaxial Josephson junctions. The velocity-matching step was observed in the current-voltage characteristics with an applied magnetic field. The presence of velocity-matching steps suggests that the biepitaxial Josephson junction is formed around a dielectric-like barrier between superconducting grains. Anomalous subharmonic voltage steps were found under microwave irradiation. The relations between anomaly steps and fluxon motion are discussed.