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We report on the microwave properties of coaxial cavities built by using bulk MgB2 superconductor prepared by reactive liquid Mg infiltration technology. We have assembled a homogeneous cavity by using an outer MgB2 cylinder and an inner MgB2 rod and a hybrid cavity by using an outer copper cylinder and the same MgB2 rod as inner conductor. By the analysis of the resonance curves, in the different resonant modes, we have determined the microwave surface resistance Rs of the MgB2 materials as a function of the temperature and the frequency, in the absence of dc magnetic fields. At T=4.2 K and f ≈ 2.5 GHz, by an mw pulsed technique, we have determined the quality factor of the homogeneous cavity as a function of the input power up to a maximum level of about 40 dBm (corresponding to a maximum peak magnetic field of about 100 Oe). Contrary to what occurs in many films, Rs of the MgB2 material used does not exhibit visible variations up to an input power level of about 10 dBm and varies less than a factor of 2 on further increasing the input power of 30 dB.