Measurements of the microwave surface impedance for high-temperature superconductor YBa2Cu3O7−x (YBCO) films irradiated by 3 MeV Au2+ ions at three irradiation doses (1010 cm−2, 1011 cm−2, and 1012 cm−2) were carried out at different temperatures (below the critical temperature of T с ≈ 90 К) and various rf current amplitudes by the use of the microstrip resonator technique. A noticeable decrease in the surface resistance and an enhancement of the linear response range at low temperatures were observed for moderately irradiated film exposed to an irradiation dose of 1011 cm−2, while at higher irradiation doses (1012 cm−2) an increase in the surface resistance and a decrease in the linear response range were observed for all temperatures below T c. These results are discussed in the framework of phenomenological theory for the microwave response of superconductors with nano-sized structural defects.