The general formula of the amphiboles of this series may be written as NaxMg2(Mg(5−y)Aly)(Si(8−z)Alz)O22(OH)2, where Mg = Mg + Fe2+ + Mn2+ and Al = Al + Fe3+ + Ti. The individual <T–O> distances are linear functions of their Al content, and the Al content is strongly ordered in the following way: T1B > T1A >> T2B >> T2A. The <M1–O>, <M2–O> and <M3–O> distances are linear functions of the mean ionic radius of their constituent cations. End-member compositions may be written as follows: A□Mg2Mg5Si8O22(OH)2; ANaMg2Mg5(Si7Al) O22(OH)2; A□Mg2(Mg3Al2)(Si6Al2)O22(OH)2; ANaMg2(Mg3Al2)(Si5Al3)O22(OH)2. These compositions define a plane in xyz space across which the data of Schindler et al.(2008), measured on amphiboles from amphibolites, follow a tightly constrained trajectory. Anthophyllite–gedrite amphiboles equilibrated under significantly different P-T conditions (e.g. igneous rocks, contact-metamorphic rocks) follow trends that diverge from this trajectory, with greater Na and Al contents and relatively smaller Al contents. Detailed examination of the local bond topology involving the A and M2 sites indicates that the maximum degree of bond-valence compensation will occur for incorporation of ANa and M2Al in the ratio 4:10, and hence 2.5 ANa = M2Al in these amphiboles. This relation closely fits the data of Schindler et al. (2008), suggesting that the variation in chemical composition in anthophyllite–gedrite amphiboles is strongly constrained by the anion bond-valence requirements of the Pnma amphibole structure. We further suggest that different compositional trends for orthoamphiboles equilibrated under different P-T conditions are the result of the valence-sum rule operating with (different) bond-lengths characteristic of these P-T conditions.