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We investigate the nonlinear behavior of magnesium diboride (MgB2) coplanar waveguide resonators in order to identify the basic mechanisms limiting the performance of polycrystalline MgB2 films in microwave applications. In particular, we focus on several kinds of switching response. Switching is observed due to increase of rf currents above a given threshold or to application of dc fields. In the former case a thermic model is able to account for the observed behaviors, including the presence of a thermal bistability regime. In the latter case, penetration of vortices at low fields is demonstrated and the effects of thermo-magnetic instabilities at higher fields are described.