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<jats:title>Abstract</jats:title> <jats:p>Strongly peraluminous granites (SPAGs), with 1.20 &lt; A/CNK &lt; 1.30, are relatively rare rocks. They contain significant modal abundances of AFM minerals such as Bt-Ms-Crd-Grt-And-Toz-Tur-Spl-Crn of potentially magmatic, peritectic, restitic, and xenocrystic origin. Determining the origin of a SPAG depends to a large extent on establishing the correct origin of these AFM minerals. Strongly peraluminous granitic rocks can form in eight distinctly different ways: (1) as the melt fraction resulting from dehydration partial melting of peraluminous metasedimentary rocks; (2) as the bulk composition of diatexitic migmatite resulting from extensive partial melting of peraluminous metasedimentary rock; (3) as a diatexite modified by incomplete restite unmixing; (4) by bulk contamination of a less strongly peraluminous granite magma with highly peraluminous metasedimentary rocks; (5) by selective acquisition or concentration of AFM minerals by a less strongly peraluminous granite magma; (6) by fractional crystallization of quartz and feldspar from a less strongly peraluminous granite magma; (7) by removal of alkalies (Ca, Na, K) by release of a suprasolidus aqueous fluid from a less strongly peraluminous granite magma; and (8) by subsolidus hydrothermal alteration of a less strongly peraluminous granite rock. Contamination by pelitic material is the most effective process for creating SPAG plutons. A detailed case study of the South Mountain Batholith shows that its early SPAGs contain high modal abundances of Bt-Crd-Grt, largely of external origin, whereas its later SPAGs contain high modal abundances of Ms-And-Toz, largely the products of fluido-magmatic processes.</jats:p>