Abstract: The water-undersaturated melting relationships of an orendite (with 1.23% H2O as shown by chemical analysis) from the Leucite Hills, Wyoming, have been determined at pressures up to 30 kbar. The dominant liquidus and near-liquidus phases are leucite, olivine, orthopyroxene, clinopyroxene, and garnet. Leucite is stable only at pressures below 5 kbar, but at 27 kbar, minor olivine, orthopyroxene, clinopyroxene, and garnet crystallize simultaneously at or near the liquidus. The following reaction relationships occur with falling temperature in the orendite magma: (a) a reaction between olivine and melt to yield orthopyroxene at pressures above 12 kbar; (b) a reaction between olivine and melt to yield phlogopite at pressures below 12 kbar; (c) a reaction between olivine, orthopyroxene and melt to yield phlogopite and probably clinopyroxene at pressures above 12 kbar; (d) a reaction between leucite and melt to yield sanidine at pressures below 5 kbar. Electron microprobe analyses demonstrate that the ortho- and clinopyroxenes crystallized from orendite are aluminium-poor; the clinopyroxenes contain insufficient aluminium to balance sodium and titanium (Al < Na+2Ti) and these elements must either be partly balanced by (undetermined) chromium or ferric iron or be involved in substitutions which do not require trivalent ions for charge balance. The experimental results indicate that relatively silica-rich potassic magmas such as orendite form under water-undersaturated (essentially carbon dioxide free) conditions at pressures of about 27 kbar by small degrees of melting of phlogopite-garnet-lherzolite or by larger degrees of melting of peridotite which has been enriched in potassium and incompatible elements. The peralkalinity of some potassic magmas (such as orendite and wyomingite) could reflect a primary geochemical characteristic of the source rock, but could also result from the melting of phlogopite in the presence of residual pyroxenes. The association of silica-poor, mafic madupites and relatively silica-rich orendites and wyomingites in the Leucite Hills can be explained in terms of the relative effects of water and carbon dioxide on melting processes within the upper mantle.