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We have measured detailed I-V characteristics of small areas of YBa2Cu3O7-δ films, which exhibit structure associated with individual Josephson junctions within the film. Both hysteretic and nonhysteretic junctions are seen. A simple model relating the voltage steps to the junction properties is developed. The temperature dependence of lc for the hysteretic junctions fits that predicted for quasiparticle tunneling junctions between conventional superconductors.