Abstract The magnetic-field-induced variations of the microwave surface resistance, R s , have been investigated in ceramic Mg 1− x (LiAl) x B 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.