We present a study of the electrodynamic response of MgB2 pellets and thin film samples exhibiting critical temperatures ranging between 26 and 38 K. We have performed accurate measurements of the surface impedance ZS =RS+iXS as a function of the temperature and of the magnitude of the electromagnetic field. The temperature variation and the field dependence of ZS was measured by a dielectric resonator cavity technique in the microwave region. In particular, the temperature variation of the

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... etic penetration depth was also determined in the RF region by a single coil mutual inductance method. In the case of the films, for T<TC/2 a clear exponential behavior of the penetration depth is observed, which can be explained by a simple BCS s-wave model with a reduced value of the energy gap. On the contrary, pellets show no evidence of saturation, and the experimental results strictly follow a quadratic dependence down to the lowest temperatures. This behavior can be induced by the presence of metallic Mg inclusions that may locally depress the gap. The analysis of the field dependence of the surface impedance in the microwave region confirms that the electrodynamic response of MgB2 is dominated by different sources of dissipation, depending on the sample history, likely to be ascribed to the predominance of grain boundaries or normal regions on its surface.