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High-resolution electron microscopy can be used to differentiate between two structural models of long-period ordered alloys. These models differ in the nature of the disorder as seen in the stacking irregularities which can have planar boundaries as exemplified by Ag3Mg or wavy boundaries as in AuCu II. In the composition range 22-27 at.% Mg, Ag3Mg is built up with a regular arrangement of two kinds of structural layers, 1 or 2 L12 cells in thickness. Some stacking disorder exists, but this alloy can be locally described using a space-group notation and has the character of being an infinitely adaptative structure. High-resolution images have been used to show the perfect planarity of the boundaries in Ag3Mg, thus demonstrating the way in which disorder is accommodated in this alloy.