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The nonlinear microwave surface impedances Zs = Rs + jXs of three epitaxial YBa2Cu3O7-δ (YBCO) thin films deposited by thermal co-evaporation on MgO substrates have been studied by the coplanar resonator technique at 8 GHz in the temperature T range 12 to 60 K in both zero and finite (∼ 10 mT) DC magnetic fields. All the films exhibited an anomalous decrease in the surface resistance Rs as a function of microwave magnetic field Hrf below 20 K. In one of the films, the application of a DC field of 10 mT has also induced an anomalous decrease in the penetration depth λ(Hrf). Analysis of the results suggests that the anomalies may be originating both in the film and in the substrate, and ways to distinguish between the two contributions are proposed. The consequences of the observed phenomena for application of YBCO films in microwave devices are discussed.