The magnetic-field-induced variations of the microwave surface resistance, R_s, have been investigated in ceramic Mg_{1-x}(LiAl)_xB_2, with x in the range 0.1 - 0.4. The measurements have been performed on increasing and decreasing the DC magnetic field, H_0, at fixed temperatures. At low temperatures, we have observed a magnetic hysteresis in the R_s(H_0) curves in all the investigated samples. On increasing the temperature, the range of H_0 in which the hysteretic behavior is visible shrinks; however, in the sample with x = 0.1 it is present up to temperatures close to T_c. We show that the field dependence of R_s can be quantitatively justified taking into account the critical-state effects on the fluxon lattice only in the sample with x = 0.4. On the contrary, in the samples with x < 0.4 the hysteresis exhibits an unusual shape, similar to that observed in others two-gap MgB_2 samples, which cannot be justified in the framework of the critical-state models.
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