A pronounced peak in the microwave (at frequency 9.55 GHz) surface resistance, R s vs. T plot (where T is the temperature) has been observed in epitaxial DyBa 2 Cu 3 O 7−y superconducting thin films in magnetic fields (parallel to c-axis) in the range 2 to 8 kOe, and temperatures close to the superconducting transition temperature T c (H ). Our data suggest that the nature of peaks observed in the two films is different, thereby indicating different defect structures in the films.