A necessary distinction is established between two kinds of long-period ordered structures: (1) periodic antiphases (PAP), whose principal characteristic feature is a continuous variation of antiphase half-period M as the composition changes; (2)'ordinary' long-period structures, which show, as the composition changes, a series of phases stable in small composition ranges, every phase displaying a different, but well-defined, crystallographic structure. It is shown, through electron diffraction studies, that the ordered Ag3Mg alloy belongs to the second kind, unlike standard PAP alloys such as AuCu, AuCu 3, Au3Cu, Cu3Pt and Cu3Pd. It is stressed that standard PAP structures can always be obtained by heating, above some transition temperature, a L 12 (or L