We report on the magnetic-field-induced variations of the microwave surface resistance, R_s, in a polycrystalline MgB_2 sample, at different values of temperature. We have detected a magnetic hysteresis in R_s, which exhibits an unexpected plateau on decreasing the DC magnetic field below a certain value. In particular, at temperatures near T_c the hysteresis manifests itself only through the presence of the plateau. Although we do not quantitatively justify the anomalous shape of the magnetic hysteresis, we show that the results obtained in the reversible region of the R_s(H) curve can be quite well accounted for by supposing that, in this range of magnetic field, the pi-gap is almost suppressed by the applied field and, consequently, all the pi-band charge carriers are quasiparticles. On this hypothesis, we have calculated R_s(H) supposing that fluxons assume a conventional (single core) structure and the flux dynamics can be described in the framework of conventional models. From the fitting of the experimental results, we determine the values of H_{c2}^pi(T) at temperatures near T_c. In our opinion, the most important result of our investigation is that, at least at temperatures near T_c, the value of the applied field that separates the reversible and irreversible regions of the R_s(H) curves is just H_{c2}^pi(T); a qualitative discussion of the possible reason of this finding is given.
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