  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.
