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The cyclic deformation behavior of extruded magnesium alloy Mg-3%Al-1%Zn (AZ31) was studied under plastic strain amplitude and stress amplitude-control at room temperature. A significant cyclic hardening asymmetry of stress amplitudes between compression and tension was observed under constant plastic strain amplitude-controlled cycling. The possible reasons for this phenomenon are discussed by a combination of hysteresis loop analysis and in situ observation of twinning and untwinning during one loading cycle using electron backscatter diffraction. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.