  We present a study on the power dependence of the microwave surface impedance
in thin films of the novel superconductor MgB2. 500 nm thick samples exhibiting
critical temperatures ranging between 26 and 38 K are synthesized by an ex-situ
post-anneal of e-beam evaporated boron in the presence of an Mg vapor at 900 C.
Preliminary results on films grown in situ by a high rate magnetron sputtering
technique from stoichiometric MgB2 and Mg targets are also reported. Microwave
measurements have been carried out employing a dielectrically loaded niobium
superconducting cavity operating at 19.8 GHz and 4 K. The study shows that the
electrodynamic response of MgB2 films is presently dominated by extrinsic
sources of dissipation, appearing already at low microwave power, likely to be
ascribed to the presence of grain boundaries and normal inclusions in the
samples.
