Internal stresses in tension and compression in an extruded and artificially aged Mg-7.7 at.% Al alloy have been determined by in-situ neutron diffraction. Measurements were made on grains having the c axis normal to, parallel to and at 62 degrees from the stress axis, and on the reinforcing phase. The results are consistent with basal slip and {10 (1) over bar 2} twinning. The second-phase particles of Mg17Al12 bear much higher stresses than the magnesium matrix does. A simple mean stress model proposed by Brown and Clarke is shown to describe adequately the strengthening due to the particles. Twinning manifests itself clearly through variations in the integrated intensity of diffraction peaks during loading. Most of the observed variations in scattered peak intensity can be explained by referring to the lattice reorientation produced by {10 (1) over bar 2} twinning. The calculated stress tensors corresponding to these intensity variations have been used to show that a critical resolved shear stress criterion is applicable for {10 (1) over bar 2} twinniing, and that the onset of twinning does not correlate with the stress normal to the twin plane. Intensity variations, which cannot be explained by {10 (1) over bar 2} twinning,occurred in cyclic tension tests. It is suggested that this is due to {10 (1) over bar 1} twinning, which yields a contribution to the grain strain tensor consistent with the direction of straining. The reason why such twinning has not been observed in polycrystalline samples by previous workers is that it appears to be essentially elastic, in the sense that it disappears almost entirely upon removal of the applied stress.