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Amplitude dependent internal friction (ADIF) was measured in three AZ magnesium alloys. Two types of experiments were performed: ADIF was measured step by step with the increasing strain amplitude and ADIF was measured after predeformation of samples in torsion. All experiments were done at room temperature. The quality factor was used as a measure of internal friction (IF). The quality factor decreased in the region of smaller amplitudes, and approaching some critical amplitude, <i>ε_cr</i>, rapidly increased. This critical amplitude increased with increasing maximum strain amplitude and predeformation of samples up to ~6%. Such behavior can be explained by considering mobile solute atoms, which may migrate along the dislocation line in the region of smaller amplitudes and perpendicular to the dislocation line in the region of higher amplitudes. A competition between dragging and depinning of solute atoms with dislocation lines may very well explain the measured dependencies.