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 π gap is almost suppressed by the applied field and, consequently, all the π-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 π c2 (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 π c2 (T); a qualitative discussion of the possible reasons for this finding is given.