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We report on the magnetic-field-induced variations of the microwave surface resistance, Rs, in a polycrystalline MgB2 sample, at different values of temperature. We have detected a magnetic hysteresis in Rs, which exhibits an unexpected plateau on decreasing the DC magnetic field below a certain value. In particular, at temperatures near Tc 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 Rs(H) curve can be quite well accounted for by supposing that, in this range of magnetic field, the p gap is almost suppressed by the applied field and, consequently, all the p-band charge carriers are quasiparticles. On this hypothesis, we have calculated Rs(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 Hc2p(T) at temperatures near Tc. In our opinion, the most important result of our investigation is that, at least at temperatures near Tc, the value of the applied field that separates the reversible and irreversible regions of the Rs(H) curves is just Hc2p(T); a qualitative discussion of the possible reasons for this finding is given. [ABSTRACT FROM AUTHOR]